Third party software means any software not made by Palm or included with the device. Sometimes 3rd party apps can cause syncing problems but generally not games like Bejeweled (which is often bundled with Palm PDAs!). Apps that do their own syncing or hack/enhance the built-in apps that do sync (calendar, address book, to-do) can sometimes cause problems. It's also easy for tech support to blame 3rd party apps because they're variables outside "fresh from the box and guaranteed to work" experience.
What other apps have you downloaded and installed onto the LifeDrive?