I've actually made offers on Fannie Mae REOs, and I ALWAYS use my own title company. Most banks will balk initially at the idea of you using another title company--as long as they have to pay. Many of them are open to it if you tell them you're paying for that expense.
If I were you, I'd insist on using my own title company, because problems occasionally arise when you don't. For example, Countrywide (and a few other lenders [which I don't remember at the moment]) specifies in the verbiage of its addendum that its title company can give the buyer a title abstract in lieu of a clean and free title. Although the 2 are closely related, they're not exactly the same thing, and there are legal implications for accepting one versus the other. (You'll need to check with a title attorney if you want to know what the difference is between the 2.)
Also, many in-house title companies (for the banks) are just as overloaded with cases as the loss mitigation department (the one's who handle the [pre-]forclosures and REOs), so you don't want your closing to contain the OOPS (due to someone's rushing around). After all, the closing agent/attorney is supposed to catch things that the lender, your realtor, you, and any other involved parties missed--before you close.
An improper or sloppy closing could end up costing you thousands of dollars down the line. (I learned that from one of my mentors [who happens to be a title attorney].)
I'll also include a link for a private lender who insists on using a title company from its approved list. I've also worked with others that have similar requirements.