Syncing iPhone with two computers - a PC and a Mac

I found myself facing this ridiculous problem. I normally sync my iPhone with a Mac. I did not even have iTunes installed on a PC until today. I needed to get a book from NY Public Library for a book club study, and they only had it in audio (.wma). Turned out that to download it, I needed to install OverDrive Media Console. It does not play .wma on a Mac, so I installed OverDrive on a PC and downloaded the book. The files of the book are protected from copying or converting, so I cannot open them in iTunes or elsewhere - only in this OverDrive Console.
Now goes the silliest part. To transfer the book to the iPhone, I am supposed to install iTunes, check "manual sync" in the Summary of the iPhone, and then select to import from OverDrive. But lo and behold, if I try to check "manual sync", iTunes says I can only sync my device with one computer, and to proceed, it will delete all stuff on my iPhone.
What am I supposed to do? It seems a mission impossible. Any ideas?

Until iOS 5 came along, iPhones were tied to a particular computer (Mac OR PC), that is to say a single machine. Pick one and sync it (or re-set your iPhone to be a "pure" iOS 5 device with no ties to either machine).

OverDrive is available as an app for iPhones -- I have it on both of mine.

chas_m said:

re-set your iPhone to be a "pure" iOS 5 device with no ties to either machine

Click to expand...

Could you please tell me how to do it? I have iOS 5 on my iPhone.

Update: I installed OverDrive app on the iPhone and was able to log in to the library from the iPhone, but it says that none of the titles in my checkout are available for direct download. Has to be downloaded to a computer and then transferred to a device.
What a quest.

It can be downloaded to your Mac. Once you install the app try downloading the book from there

Mini_mi said:

It can be downloaded to your Mac. Once you install the app try downloading the book from there

Click to expand...

It cannot. I get a notification that .wma is not a supported format.

I got a response from the library's technical support that they do not have a solution for this problem. OverDrive can only download .wma to a PC computer; iPhone can only by synced in a manual mode with one instance of iTunes; so they don't see any options how I can upload the book without erasing everything else on my iPhone.

@chas_m: how do I set the phone to be not associated with any particular machine?