Actual MSF instructors chime in here to correct me, but here's my $0.02:
Things like this often arise because we've heard or been taught something and didn't fully understand it.
The MSF course teaches us to stand the bike up and THEN brake to stop in a corner. Connect the dots and what you wind up with is "don't brake while leaned over." Take that to its logical conclusion and you get "never brake in a corner." But if memory serves, they never actually say that.
It pays to understand the purpose of the Basic Rider Course. It's there to teach you skills that will keep you out of trouble... things like "don't cover the brake lever." But it's obvious that if you DO cover the lever you can react faster. So why do they teach that?
IMHO it's because total beginners -- the target audience for the BRC -- are far more likely to panic than experienced riders if something goes wrong. That means that when the **** hits the fan they're likely to do something dumb like grab a fistful of brake, lock it up and crash. So the instructors teach you skills that will make that less likely to happen. But once you've got a lot of experience, those "safer" skills become less relevant. That doesn't mean they're wrong. It does mean that as you develop as a rider, you pick up new tools to work with -- tools that are not part of the basic course.
Take this to the braking in a corner thing. Most if not all of us have heard of the "traction pie." You've only got so much traction, and it has to be distributed between cornering, braking and acceleration. Exceed the limits and the tire gives up. Brake, and there's less traction available for cornering. Corner harder, and there's less traction available for braking. Brake too hard and corner too hard at the same time, and you've blown your traction budget. Result: Crash.
Easy to see how this concept could be interpreted as "never brake in a corner." But that's not true. Racers routinely trail brake, as do experienced riders. It's a useful skill, but as noted it's something you need to learn and not be ham-handed with. What you do NOT do is brake HARD while leaned over.
The reason (IMHO) that MSF teaches you to stand up before emergency braking in a corner is that by standing the bike up, you're maximizing the traction available for braking and therefore giving yourself the best chance of getting out of a tough situation in one piece.
If you understand why things work, you can make smarter decisions. Beats blindly following rules you do not understand every time.
Knowledge is power.
PS: At my last track day I encountered the EXACT MSF emergency brake in a turn scenario. Here it is on video... note that without thinking, I executed a textbook MSF BRC maneuver. Stood up and braked hard. What do you think would have happened if I'd tightened the turn to avoid the wreckage AND braked hard at the same time?
Link to original page on YouTube.