1) this guy lies the whole day long if he deems it necessary without any regret at all
2) he technically didn't lie ... he was a guardian and not a Yotsuba -
true, but that doesn't matter at all since Mayumi doesn't know about that. She might perceive it as a lie nonetheless. Emotions like sadness, feeling betrayed etc. are triggered by what she believes to be true and not by the truth.
3) I assume the bigger problem and true reason for the emotions she seems to have on the cover is the family Tatsuya belongs to and his engagement.