No, that's not the reason.

It has to do with how Rolex USA was set up. They are not a subsidiary of the main Rolex Company but of a Rolex Sub-Branch so technically a Rolex bought in Europe is not a genuine Rolex according to Rolex USA and therefore is subject to seizure. Even if you travel with your Rolex you better have only one because more than that and it can be seized unless you can prove it was bought in the U.S. A few exceptions do exist like for watches bought in a military PX but only one watch per serviceman and entry in the U.S for a Rolex is one per person.

I don't know how watch parts or repaired pieces are treated.