(I'm the author of the code you linked to.) To the best of my knowledge, the code is correct (and I'm sure that the high-level algorithm of using Gaussian elimination over GF(2) is correct). The solution it produces is guaranteed to solve the puzzle, though it's not necessarily the minimal number of button presses. The "efficiency" I was referring to in the writeup refers to the time complexity of solving the puzzle overall (it can solve a Lights Out grid in polynomial time, as opposed to the exponential-time brute-force solution of trying all possible combinations) rather than to the "efficiency" of the generated solution.
I actually don't know any efficient algorithms for finding a solution requiring the minimum number of button presses. Let me know if you find one!
Hope this helps!