Lots of different arguments going on here. Language is such a messy thing. And the fact that we have to use language to talk about language and since everyone's understanding and definition of the words we are using are slightly different one from another, it gets really messy. It seems, though, that most people are on the same page in general.
I think one semantic problem point is saying "using a textbook" and people understanding that differently--is it in a classroom context, is it for self-study, is it for sentence mining (who the hell came up with that anyway?), is it as a resource, etc. Even if we all have slightly different understandings, if each of us can maintain consistency with our own arguments, over time we might gain a better understanding of each other.
Tobberoth, the example you gave doesn't really match your subsequent explanation. You first set up a situation with straight (decontextualized) textbook study vs. straight (contextual) input. Then you go on to say that textbooks should be used in conjunction with input. It somewhat confounds the situation. But given that most of us second language students use an eclectic approach to language study, it's not that confusing. But to analyze a bit further the example you gave...
After pitting textbook against input, you set up a decontextualized test to see which one would do better. In teacher school, one of the things I was taught was "assess/test the way you teach". In other words, you shouldn't teach math by doing lots of problems and then have a test where they have to write an essay elaborating the details of the formulae they have been studying; you should test by giving them more problems. So, of course, the textbook person will fare better on a test set up the same way as the textbook, that is, designed for the purpose of artificially conjugating verbs. However, if the input person were to conjugate iku as you proposed, I, as a language teacher, would could that as a HUGE success. That's a stage that exactly mirrors a child learning their first language. In my class (yes, input is applicable to the classroom), that would tell me that I've given enough input of regular -ku verbs, but I've been neglecting input of irregulars. Easily remedied. More iku!
How about a test using the language naturally? Give a picture that the students must describe. Have a conversation with the students. Check use of conjugations in context. See who fares better. I'm guessing, both would have trouble given the short amount of study, but I would say both would do about equally. The input student might have an edge given more exposure to a variety of vocabulary rather than lists of conjugated verbs. How about a test a week later, then a month later, then a year later? I would wager the textbook student would decrease in skill much more quickly than the input student (given no further textbook/input respectively). (This is the power of stories Heisig has harnessed put to a different use. Input usually comes in context. That context is often a story. Stories help things stick because they have a plot and they often evoke emotions and feelings. The things that stick include vocabulary, grammar, tone, register, etc.)
Even setting aside this example that you created, I take issue with some other parts of what you say, Tobberoth. I wish I knew how to use the quote function and I'm a bit tipsy so I'm not going to figure it out now... but anyway. You said that one should learn the basics fast and then move on to input. I agree and I disagree. If you mean learn the basics as in memorize rules and conjugation patterns of 'basic' grammar to completion, then no, I don't. If you mean read through a textbook to gain a general understanding of the layout of the language and the various types of words and their forms before seeking input, then yes, I do. In general, your posts and your tone make me think you find it important to have the rules memorized well before moving on. I think somewhere else you question why this is a bad thing or would be wrong. Well, it's counter to the whole idea of using input. Textbooks (used in the traditional way) and input don't really go together. If you want input to be your guide, then in a way you're taking on the way input works. With input, there is a natural order of acquisition. (This order is not something to be followed; it's simply a description of when people acquire different parts of language.) The general rule is you acquire things faster if they have more meaning. So of course nouns, verbs, adjectives carry much meaning so they are the fastest/easiest to acquire through input. Conjugations carry less meaning so they come later. Etc. So if you want input to work for you, you shouldn't be shoving things in your head forcing yourself to "learn" them out of order. If you want to use input, you might consult a textbook so you can orient yourself when you find language in the wild. When you can start making sense of things, you might return to the textbook. Re-reading it your mind will latch on to new things (things you actually read before, but only now your mind is ready to understand) and you will then be able to understand more language. This back and forth is helpful but only insofar as the grammar explanations are providing meaning to the language. And yes, the analytical part of the adult brain can comprehend how language functions and how various grammatical features function and how forms of words change, but it doesn't mean that the language part of the brain has instant access to this information. That's why book learners generally speak haltingly but possibly with great accuracy but input learners can speak more fluidly but possibly with many errors (though successful communication is achieved by both sides).
You did bring up the point that if you want to speak sooner then a textbook will get you there. Ok, but can you understand responses to what you say? What kind of conversations can you really participate in? Is speaking sooner a good idea? What situation requires you to speak to such an extent at an early period in your studies? What can a textbook provide that memorizing some key emergency phrases/vocabulary can't? Are you imagining a situation of being in Japan and needing to speak early? Like I said before, it's easier to acquire more meaningful parts of language (even if you are using a textbook). And those meaningful parts of language can take you a long way. Let's say you want to say you went somewhere yesterday. If you spent time studying a textbook, you might say "ikimashita" or "itta" or you might say "iita" by mistake. But if you learned some key vocab, you might say "kinou iku" and use gestures to get your meaning across. I guess what I'm trying to say is that I can't imagine a real situation where you'll NEED to conjugate accurately in the case you are required to speak early in your studies. Learning to conjugate fast to speak early just gets one into bad habits. It makes one think that language needs to be used consciously. That's not how natural language works. It should just fall out of your mouth. So really it's not good no matter how you do it to speak before it falls out of your mouth. Speaking serves to make your speaking more fluent and to solidify your grammatical knowledge, whether that knowledge is accurate or not.
Sorry, I rambled. Tend to do that more when I've been drinking.