To be preciese the limitation is one
library rather than one
computer. Perhaps at some point you'd copied your library from one of your computers to the other. If so, even if the content of the different copies of the library then changes, they will contain the same
LibraryPersistentID and iTunes won't issue warnings when you switch between different copies to manage the content. What you may not have noticed however is that any content manually added from one library will be removed if you update the
iPhone or an
iPad from another library that doesn't also contain that content. I don't know
why Apple introduced this unnecessary restiction but it's nothing to do with disc mode whatever you might read elsewhere... It is however a limitation imposed via iTunes, not the iPhone firmware, as iTunes is in charge of all data transfers between the library and the device. Perhaps one of your libraries got corrupted and was rebuilt with a different, newly generated LibraryPersistentID.
To sync your iPhone using which ever computer you want simply move your entire library out to an external drive and connect to each computer as and when you want to use it. In practice I use
SyncToy 2.1 to clone my library at home to a portable drive, take it to work and use SyncToy to clone the library to the local drive. Each computer opens the local copy rather than the one on the external. The upshot is that I have three copies of my library as security against data loss and the freedom to update any of my family's iPods & my iPhone from any of my computers.
tt2