Power of Capture-Check: Incorrect Solution

Course FM Schiller - "The Power oft Capture-Check", Lesson WCD005, Furman-Konstantinopolski, 1948, is incorrect.

The solution according to FM Schiller is: 1.Rxg7 Kxg7 2.Qc3 Kh6 3.Rxf7 Kh5 4.Nf6 Kh4 5.Rg7 Qxf4 6.g3 Qxg3 7.Qd4 Re4 8.QxRe4 Kxh3 9.Bf1 Qg2 10.Bxg2
There are other solutions and even better ones, which are "incorrect" according to Schiller. nI detail:
a) 2..Rxe5 best for Black according to Houdini
b) 4.Qg2 and 4.g4, best for White and Mate in 6, according to Houdini, but "incorrect" according to Schiller;
c) 5.Be2, also mate in 6, according to Houdini, but "incorrect" according to Schiller;
d) 6.Be2, also mate in 5, according to Houdini, but "incorrect" according to Schiller.

Finally, there are no helpful direct hints and variations at all.
The course is rather frustrating in that way and the worst one I´ve tested up to now. All other courses, I looked for, were great.

how did a) 2.....Rxe5 get there ? you mean .....Re5 ?

Thanks, I have added some of these solutions as alternate correct moves. The author tries to use capture-check solutions to reinforce his point of the course and Black as the losing side does not need to play the best moves.

Hate to say it, but much of the original Chess Mentor course (not the new stuff that chess.com staff have added) is filled with inaccuracies, errors, and less than helpful explanations (if any at all are given) of why moves are wrong.  I don't care; I still love it although I'm beginning to think it's addictive!

Hi all, 
thanks for the many answers and corrections.
I agree with you about the moves from black side (2..Te5 was not the problem).
I agree also about the aspect, to reinforce the point there must not be always the best moves, and I know this from other courses. The problem here was:
a) many mistakes, b) there was no point in FM Schillers solution, because there were simpler (easyer) and faster ones (it was in no means understandable for me, why he choose this solution and classified othes as incorrect), c) the direct hint gives no help, so the player finally is completly helpless and must guess the solution, d) from a pedagogically and psychologically point of view it´s rather frustrating, when you become constantly the answer "incorrect"while proposing good solutions and get no variations at all. I must also say, to clarify his intention, the author gives possible checks und captures in his explanations, but constantly some are missing and it is not clear, why he mention that ones and others not. 
Concluding, errors in lessons are no problem for me. I´ve posted this, because i come to the conclusion, the course (up to this lesson, then I quite it) tends to have problems of that kind throughout, and I think, chess mentor would completely not functioning in that way. Fortunately I can say, the other courses, I´ve checked, are great and handle this kind of aspects pretty well. So, chess mentor is a fantastic training tool and possibly the very best, I´ve seen up to now.