Well, if you look at the Windows platform the backup procedure takes advantage of shadow copies and that works actually pretty smooth. Same technology should be applicable in backup softwares on OS X.
That is exactly the difference. Windows itself has the ability to take volume shadow snapshots, i.e. right now, snapshot the state of the entire disk (new writes go elsewhere) and back it up at your leisure. I don't think OS X has this capability, it's only at the file granularity - multiple files are not guaranteed to be in sync (which is precisely the problem with trying to use Time Machine on a running VM). The entire disk vs per-file distinction is very important. It doesn't matter if we're talking about Fusion, Parallels or VirtualBox or even non-virtualization, the problem is at the OS layer.
Could OS X theoretically do this? Of course. Could some backup software do this? Maybe, it's probably harder - you'd need kernel hooks at least, as you need to intercept all writes. Should Fusion do this? Probably not - it's a failure in OS X's abilities, and not at all related to the core problem of virtualization.
