Could it be that there is a Type 1 font on her machine along with the OTF? I'd try packaging the file and see which fonts get collected. It could also be that there is some residual info in the file that could be cleared out with a save-as, or a trip through IDML. I'd try that first. And often when I get a file from a co-worker and it has a stray font, it turns out to be assigned to something like a space or a return. You can find those with Find Font in the Type menu.
She just recently purchased Gotham from Hoefler Type. Neither of us had it on any computer before this, so I don't see how that's possible. In fact, when I load the entire Gotham suite into Suitcase, it displays as "OpenType - PS" under Type. That "- PS" I'm assuming stands for PostScript, as outlined here: OpenType Features & FAQs | Adobe Type. If I understand this, The OpenType font files have PostScript contain PostScript font outlines.
What I'm struggling with is how the exact same font files can load on her machine one way and on mine in another, because that's what seems to be the case here.
Has this problem been solved? I am having the exact same problem, only mine is with a job I need to work on remotely on my laptop and then at home on my Desktop. It's amazingly frustrating!!