The joint use agreements extend to greater granularity than the towers. Agreements are frequently arranged to place antennas on other provider towers. The use of Verizon as an example should have been further qualified to the level of antenna placement or other compatible antennas on those towers. The cell network is far more complex and in place with sharing agreements to control investment and to keep the number of towers to a minimum while achieving adequate coverage. Placement of towers is controversial in all communities. Customers want adequate coverage, but not the physical tower in their back yard.
So, yes OnStar can get service off a Verizon Tower, if that tower has a compatible antenna through a joint use agreement and many do have that in place.
The cell providers may compete for customers in their advertising, but behind the scenes there is a great deal of cooperation to provide adequate coverage as mandated by the FCC with the fewest number of unattractive towers.
On a recent vacation on the island of Kauai, the tour bus driver pointed out a Verizon Tree. It was a Verizon cell tower covered with artificial evergreen bows in an attempt to make it blend in with the scenery. It did not come off very well aesthetically, but my AT&T cell phone worked just fine getting service from that tower (obviously with the appropriate antenna).
2015 GMC Canyon SLT 4x4, Onyx Black, Fold-a-Cover