I agree that it would be up to the specific contract whether they'd be allowed to throw other equipment in addition to their sponsor's equipment. However, I feel like the point of company X's ball staff is to promote the company's equipment, to make it visible to other bowlers. Being on RG's ball staff, to me, means you should be throwing RG balls.
When Lonnie Waliczek was on the Circle staff a few years ago, he was not exclusive, he could throw other equipment given that Circle had such a limited lineup. He made the telecast, in fact, wearing a Circle polo but threw a 40-year-old Zone X on the show.
"But Roto and Storm are the same company!" Well, Track and Columbia were the same company as well but you didn't see Chris Barnes throwing Track or Wes Malott throwing Columbia (this year). Same for Ebonite and Hammer. If you say you're going to promote and use RG balls as part of the RG ball staff, I think you should.
SH