*shrug* Experiences vary. I can understand someone thinking that the invisibility of their mental illness is a privilege because they don't have to deal with people assuming they are [insert stereotype here]. I can also understand someone else with different experiences disagreeing.
Part of the problems of the privilege model is that it focus on overall societal status over individual experiences. It would be fucked up if she said that everyone with bipolar/"invisible disability" is privileged. It's less so if she's talking about her own experiences. I mean, surely she has that right?
i've seen two cases in the past. when i was (kinda wrongly) diagnosed with chronic depression, people either romanticized it ("oooh, that's a musician's muse, you must be so creative") or told me to suck it up because "it's not a real disease, like cancer". now that my original diagnosis has been revised into paranoid hallucinatory psychosis (which does have chronic depression as a frequent side-effect), people are scared of me or don't trust me, thinking i could be a serial killer or outwardly violent. i'm not towards others.
in either case, i'm just fine hiding it. i get on with my life, take my antipsychotics, and try to the best possible. the only reason i'm posting it publicly is because you've never seen me, and that's perfect. you know my train of thought, but not my face.
maybe the op has that right to view bipo as being better than being physically handicapped, but in no way should it be romanticized or worse, considered a privilege. it's a curse with no sure-fire cure. i'm resigned to the fact that if i stop taking my pills, my life will go haywire again. in practice, it's like having high blood pressure. but psychologically, it's a hell of a burden to bear. it's not fun, it's not cool, and i really wish tumblrinas would quit fantasizing about having all the mental illnesses.