Rawhide is not sinew.
Sinew is not rawhide.
What applies to one does not always directly apply to the other. For example, using Titebond with sinew really does not allow the sinew to fully shrink and pre-stress the bow back. Hide glue will allow that. Hide glue and sinew will together (generally speaking) improve a bow's performance.
Rawhide does not change the performance of a bow to any measurable degree. Feel free to use Tightbond I, II, or III with rawhide. Or use hide glue. Or use 2 part epoxy if that is something you feel comfortable with.
I prefer the faster tacking quality of TB for rawhide backing over the slipperyness of hide glue.