I understand being skeptical that the showrunners/Bethesda are going to be at all considerate of lore and characterization from previous games (Bethesda in particular is notoriously finicky when it comes to remembering their own lore) but i do also think it's a bit of a stretch to call House "out of character" in the tv show when he was only kinda vaguely agreeing with what everyone else was saying. It seems just as likely to me that Robert House, known 4d chess player, simply saw which way the wind was blowing in that room, went "oki doki sounds good to me 👍" and then hoofed it back to Vegas to begin his preparations.