I don't speak with people with no profile photo. To me it's an indication of a lack of openness & there's enough anonymity on the internet already. To answer the question as to why people want to use the webcam for conversations, watch this video:

https://www.youtube.com/watch?feature=player_embedded&v=FefFfvriAwQ

It explains why some might think it important. Especially when you're learning a new language.

So my point is that I find merit in the idea of teaching the conjugations of common verbs... adding the infinitives of others verbs & forming sentences with these, it's hardly a new approach. Nor is it necessarily quick. Plus, the prepositions tend to be the most difficult part of learning a language... all of the tiny connecting words that are necessary to not sound like a fool. In one video Tony simply says that you have to accept that after saying "empecé" you connect that with "a aprender" to say "I began learning"... it's just the way it is.  Nowhere does he teach that as a rule empezar is followed by "a" when adding an infinitive. You might incorrectly assume that all verbs behave this way. Nor does he address the idea that Spanish uses infinitive much more than gerund compared to English. It's just implied that this exception happens & by ignoring that detail, you will learn to speak much faster.

I found this method to be one of learning canned phrases with little discussion of the reasons for the decisions you're making. As a comparison I highly recommend the programs by Fluenz as a method of starting to learn Spanish. There is much more detailed explanations and there's an obvious flow & path toward fluency than other programs (Rosetta Stone for example). I find Tony's method similar to teaching math by telling you the answers to some questions and assuming that by knowing those answers you'll be able to function in the world of math. Imagine in the math question on this board (1+1+1+1+1+1+1+1+1+1+1+1*0+1=12) if I just said that the answer is 12, accept it, and didn't explain that there is an order to evaluating math symbols and the 0*1 must be calculated first before the + signs. You'd know the answer to this question & only this question. You'd have no idea why it was the answer.

I agree with Aegis. I've watched the sample videos and I just don't see how you're splitting any atoms here.  For instance, if someone wants to learn Spanish & I teach them the following:

Hola - Hi

Soy - I am

Canadiense - Canadian

de Canadá - from Canada

programador - a programmer

No soy - I am not

Eres - you are / are you

The idea that this represents "instant conversation" is a fallacy. You can now say "Hi, I'm Dave. I'm from Canada. I'm a programmer. Are you Canadian? No, I'm not from Canada" but the notion that something unique has happened is oversimplified. First of all, it's not a unique idea to teach  a few verbs/conjugations, nouns & prepositions & teach the person to connect them. It's not a "matrix", it's just a bit of Spanish vocabulary. Secondly, it ignores that fact that it still involves rote memorization. And thirdly, it's very basic & does not lead to an expansion of vocabulary the way the author states that it does. 

For example, it makes much more sense to me to teach that regular AR verbs are conjugated in the following manner:

The root is the part of the verb before the AR. Take the root and add the following endings: O, AS, A, AMOS, AN

HablO, hablAS, hablA, hablAMOS, hablAN

You now can conjugate the majority of AR verbs in Spanish in the present tense. Move on from there to list the most common regular and irregular AR verbs. 

I see you responded while I was typing.

I guess what I'm saying is that there is room for a happy medium between thinking that you must learn an infinite number of words/sentences & thinking that if you learn only those things that you think are important, you're set. I think that in order to sell the idea that people can learn a language quickly you gloss over many concepts of what makes a person "fluent". For instance, your point that in order to understand someone I need to focus on key words that I can understand... if I have no clue about conjugations I can can't pick out key verbs in a sentences & therefore will find it impossible to understand the context... take IR in Spanish for example... voy, vas, va, vamos, van... none of those conjugations sound alike so I can't simply listen for words I understand. Add to that your idea that fluency begins with my focus on words I want to say... now I'll only be able to key on conjugations of YO, which will never be used with regards to "me" as they will be using conjugations of "tu" or "usted" instead of "yo".  

I understand. But similarly, learning a bunch of words & phrases in another language while understanding nothing that is said to you is like buying a bunch of canned goods for groceries while not owning a can opener.... you're no further ahead, yet you believe you are fully prepared.

I don't agree that one must learn everything of a new language to know something. But I also think that telling people that if they learn the phrases that they deem necessary to say the things they want to say then they will be "fluent" is equally wrong. 

I've had conversations with people that know a handful of English phrases & want to talk. The problem is that they cannot communicate. They can say some canned responses but cannot understand anything said in return. I fully believe that conversing is a good step to take, but I also think that you must understand much more than a dozen phrases/sentences to get anything meaningful from a conversation. For the other speaker, it's very frustrating to speak to someone who has been told that they must start talking to a native as soon as possible.