If DC doesn't mind the side discussion, I will try to offer an explanation. One source of confusion in these kind of discussions is the different ways folks often use the same word to mean different things.
The term strain is usually understood in science as a linear measurement. For example, if a rubber band 12" long is stretched to 13", by hanging a weight on it, then the strain is said to be.... 1 inch per foot.
I hope Onebow does not mind me reforming his statement to what I think he meant.
then both the backing AND the belly are going to be subjected to 65 pounds of strain force, the back in tension and the belly in compression
With a given force, how much the sinew or wood stretches on the back of the bow depends on its "stiffness",and how much it can stretch before it breaks, is its elasticity.
Sinew of course is not as stiff as wood so it wants to stretch more than a wood back, and does so without breaking, because it can. The tension and compression forces on the back and belly are still equal.