Serious Tactics Trainer Error

It's clear to me, that TT is flawed in numerous ways, and I can prove it beyond any reasonable doubt. 

See this problem: http://www.chess.com/tactics/?id=256871

Then see my comment posted. 

I also ran the problem through computer analysis on expert (2000+) and after black's best defensive moves, black is the one with the advantage, not white. 

White CANNOT achieve an advantage from this position if black plays accurately. Therefore, the problem is flawed.

I need to make a correction to my comment. I'll just draw a diagram:

This sequence was given by the computer on expert (2000+), so it's probably accurate. Now explain to me, how exactly does white have an advantage??

Black walking into the mate is a bit daft, Houdini suggests Qc7 or Bg7 as best moves for black with near equality. However the moves in the solution for white are also the best moves given the respective positions according to Houdini, so I don't think it's a big deal. Ultimately tactics trainer is a tool to improve tactical skills and I believe it accomplishes that, so I wouldn't say it was 'flawed', although it is not perfect either.

3.Rd1, not 3.Qd3. White ends up at about +1.3, according to Stockfish DD.

It's the same with huge sacrifices. If they aren't accepted, then you just play on with maybe a slight advantage. These tactical themes can be applied as a part of a positional plan.