I believe he is telling his truth in both statements, but events were fresher in his mind on the 4th May and while I accept that there may be translation errors I don’t believe they would be of such a magnitude as to translate a whole paragraph to more or less the complete opposite of what he actually said.
The second statement is clearer, far less vague, when questioned for more detail on the shutters, curtains and window.. He is also clearer in the rogatory statement about where the light is coming from and that the curtains are closed and that there are no draughts through the room. Both statements can't be an accurate description of the objective reality with regards to the light in the room.. I believe he is telling the truth in the second one. That is my honest opinion. Yes, agree it's much much later.... but he will have thought about the details of that check almost every day.
If he had found the scene that Kate described there would be no vagueness at all. It would have been obvious that the window was open and the shutters raised and there was a draught through the room. Even his first statement does not describe this with any degree of certainty... he just "seems to think the light might be coming from outside".