This may seem like a basic question, but here goes.

If a PE kit says it is for a particular vendor, such as Tamiya, can it be used on the same vehicle from a different vendor? It would seem that PE for, say a Panther, should be useable on anyones Panther.

Thanks for your input.

Sometimes you can,it depends on how similar the two kits are. Since each set is designed to fit a particular kit, if the other kit has some dimensional differences, then they may not work.

Rob is right, most models from different companies have various dimensional issues.
For example, I have a PE set from Eduard for the Wespe from Alan. I test fitted some pieces on the Tamiya Wespe, and they don't fit. The PE parts are to small for the Tamiya kit, but fit perfectely with the Alan model.
Same goes for the Pzr IV. The Dragon kits are smaller than the Tamiya kit, which should not be surprising, as Tamiya has always build their models on the 'chunky' side.

Go with the recommended manufacterer, and you won't go wrong.

Cheers
Henk