When you have a font installed on your system, but the website you're visiting is using google fonts (in this case Muli), does IE9 load up your installed font file, or the one from Google?
In other words, how does IE9 prioritize which font file to load if there are two available with the same name?
EDIT:
I think the answer is that it uses the downloaded version of the font. I installed Muli and then used fiddler to watch the site and it downloaded the .eot
I'm not 100% sure that's right but it seems like it is. Doesn't explain why my client's fonts look ~ever~ so slightly different than mine, but she has some other issues I can't replicate so it might be a larger issue than just fonts.
Start IE, load the page (either locally or by internet), press the F12 key, click the Network tab, click the Start Capturing button, refresh the page. Does your font file appear within the list? If not then it is probably loaded from the OS and not from Google.