You can't often control what you are given (sometimes not at all), but one of the downsides of working on the PC is that the Mac TT and PS fonts won't work for you on their own (maybe they can be re-jiggered, but that will likely violate the EULA from the font maker). If you were on a Mac and the roles were reversed, you could use PC fonts, but that's beside the point. The best case scenario is if the files were set using Open Type fonts, since they are cross-platform compatible. I know this doesn't offer any fix for your problem, but I just wanted to throw it out there.
There are versions of fonts that are different but have the same name, and I'm guessing this may be part of your problem. Even if you have the PC version from the same foundry as the Mac version, there may be differences. I'm not even close to being a font expert, so I can't tell you how it all works under the hood, but I imagine you are seeing pink because even though the font names are the same, the code is different, so the PC/InDesign is telling you you don't have the right font. The only option is to see if you can find other versions of the font that will work.
And lastly (this may be a stretch), are there any character styles applied to this text that may be mucking it up?
Over on the ID Scripting forum there is a thread you might check out: Finding Unassigned Glyphs. There's a link to Peter Kahrel's script at the end, but I found some of the preceding discussion useful.