Aha, I figured it out.

When the board has tens paired and a 4 hits to counterfeit the deuces, then the king on the board is the high card and hence our Queen and Jack are meaningless and this then creates a split pot. With the kings being the pair on the board, then if the four hits to counterfeit the deuces, then suddenly our queen high is relevant and wins us the hand. So there, I have explained the discrepancy between the two different boards with the tens paired and the one with the kings paired. Now I may rest and fall asleep like a normal person would have done many hours ago.

Alas, I define the maximum number of possible outs to be 25.