This is right. In 2003. Times have changed.
The Touch will actually let you sync with more computers more easily than other iPods. Although others can match up with more than onePC/Mac, also. You probably do have to leave auto-syncing off, but I'm not sure since I've never had it on for any iPod.
With some previous generations of iPods (most that I've worked with) there were 2 possible ways to format the internal storage of the iPod - either Macintosh, or Windows. (Presumably, but not explicitly stated, Macintosh was a pseudonym for HFS+, and Windows was a pseudonym for FAT32.)
If you plugged a Macintosh-formatted iPod into a Windows computer, you could not do anything else with it until you reformatted it for Windows.
Conversely, if you plugged a Windows-formatted iPod into a Macintosh computer, you had the option of continuing to work with it without reformatting it.
I always supposed it worked this way because iTunes was silently accessing the older generations of iPods indirectly by mounting certain filesystems using the host OS's native removable mass storage interfaces, and Windows didn't have support for mounting HFS+ volumes.
I suppose Apple did not have the luxury of continuing this way of doing things with the iPod Touch because of the fact that embedded OS X required its filesystem to be a Unix-friendly one like HFS+ exclusively.
Therefore, they needed to introduce a different synching mechanism to get the files across irrespective of the host computer's filesystem capabilities.