I respectfully disagree with your respectful disagreement. ;P
Then we may have to agree to disagree on this one!
If the traits of "dumb and flaky" are denigrating to a woman (or a man), then the traits of "not-dumb and not-flaky" cannot, by definition, be equally denigrating. So, it's not sexism - it's plain old stereotyping of character traits, neutral as far as gender is concerned.
But my argument is not like-for-like comparison of stereotypes, as you've described (flaky vs. not flaky), because in that respect you're right.
But say we have two scenarios: scenario A and scenario B. In scenario A, we have the male protagonist Bob and female protagonist Alice. Both work for the same company, but Bob is outgoing and has lots of friends while Alice is quite reserved. The writers of this show, based on these archetypes, make Alice painfully shy and a stickler for her work, whereas Bob is a flirt and gets away with practically everything because he's charismatic.
And together, they fight crime!
Now in scenario B, it's the other way around: Alice is the outgoing and popular one and Bob is the reserved type. In this case, the writers make Alice loud and obnoxious and a bit of an air-head, while Bob is clumsy and spends most of his free time in front of his Xbox.
Doing a like-for-like comparison would give the results you describe: Alice A, who is shy vs. Alice B, who isn't. Alice B, who is a 'bimbo' vs. Alice A, who isn't. However, stereotypes emerge from the archetypes on which the characters are built, so while over-use of Alice A in a tv show could insinuate that any female in real life like her would be impossible to socialise with and anal about their work, the use of Alice B in popular media would mean a female like Alice B in real life wouldn't have the negative stereotypes of Alice A (and you could call these stereotypes sexist, as in this hypothetical situation Bob B's stereotypes are different) but would have their own negative connotations based on Alice B's character.
Clear as mud? If you can make sense out of it, that's the reason why I don't believe character role reversal cannot be sexist; each archetype presents its own unique stereotypes, and they're often gender-based. I know that the hypothetical situation I've just written is completely fabricated, but to a lot of writers the archetype of, say,
nerdy best friend (female) has its own female-exclusive negative connotations that
nerdy best friend (male) does not, and as such can be seen as sexist.