It is false that there is a strategy-stealing strategy for white. It would need to cover EVERY black response.
No it would only need to occur at any one point in the game.
Strategy-stealing is a way to construct an ENTIRE STRATEGY for one player from a strategy for the other player. This means a decision process for every position that can arise when executing the "stolen strategy".
I don't call it strategy-stealing.
Your post discussed what had previously been referred to as strategy-stealing using the pronoun "it". Do you not understand how communicating in a language works?
A chess strategy is a decision process that suffices for all positions that can arise against any opposing play. i.e. it picks a move in every position that can arise when applying it.
I hope seeing the definition helps you.