In the fiction of the show Murphy Brown, Murphy can sneak into the White House and lecture Sarah Huckabee Sanders. In the reality of the world we live in, though, that's errant nonsense.
I try to avoid watching her as much as possible, but yeah, it did seem unlikely that any White House press secretary would just stand there passively while a reporter hijacked the whole conference like that. Of course, their choice to use stock footage of a real person and a voice impressionist limited how much "Sanders" could do. I know the show has always poked fun at real political figures, but it might've been better from a plot structure and comedy standpoint to use a fictitious press secretary character, a
roman a clef for the real thing like "the Wolf Network," so that they would've had more freedom to let her clash directly with Murphy. (How ironic that this show airs immediately after an Allison Janney vehicle.)
Also, I'm not convinced the situation would've happened at all. I can buy that the Murphy Brown I remember would get so caught up in her determination to defeat a White House press room ban (a situation she was in more than once on the original show, IIRC, so it's sort of her white whale) that she'd forget about her son's opportunity and all that. But it is a bit hard to believe that it all happened so swiftly. It seems more likely that the process of her seething over it, deciding to act, trying to get around the ban legitimately, deciding to break in, convincing everyone else to go along, and making the arrangements to fake credentials would've taken at least a couple of days longer than it did, so that it would've been after Avery's debut and the whole personal conflict would've been avoided.
And come to think of it, if she was only banned from the press room after her Twitter war with Trump last week,
why didn't she say these things to Sanders before now?? I guess the idea is that it's because she wasn't active in journalism again until the premiere last week, but still, the fact that she was banned from the press room implies that it's a change in her status and that she was allowed in before. So it doesn't quite fit together.