This NOTE (found under Rule 9) states the following:
Anyone who uses a plural verb with a collective noun must take care to be accurate—and also consistent. It must not be done carelessly. The following is the sort of flawed sentence one sees and hears a lot these days:
The staff is deciding how they want to vote.
Careful speakers and writers would avoid assigning the singular is and the plural they to staff in the same sentence.
Consistent: The staff are deciding how they want to vote.
Rewriting such sentences is recommended whenever possible. The preceding sentence would read even better as:
The staff members are deciding how they want to vote.
The three given options:
Flawed: The staff is deciding how they want to vote.
Consistent: The staff are deciding how they want to vote.
Even better: The staff members are deciding how they want to vote.
Question (1 of 2):
Would you agree with those general assessments? As I understand them...
The 1st is flawed because it's inconsistent (re: they/is).
The 2nd is consistent, but such sentences should be rewritten whenever possible.
The 3rd is even better, specifically meaning it reads better than #2.
Question (2 of 2):
If #2 isn't flawed in some way, why should it be rewritten? Either it's idiomatic (somewhere, I suppose) or it's not.
I'm not sure if that's about grammar or a writing tip.
Update: I've seen the workaround option (#3) being suggested as though it were preferred, presumably, by most AmE speakers (but not BrE; this is a case where they differ, according to the BBC grammar site).
Note: I no longer use this source (GrammarBook.com), but I see no way to work it out of this particular question.