This is more complex than it may seem. When you have both ends "pinned" the forces in reality are quite complex and not easy to model. Spine's physics constraint is very efficient, but it is not modelling forces like reality or even like a fully featured physics engine. The tradeoff is there are some things we can't do, like pinning the end of a chain.
As with many things in 2D, there are various ways to fake it. There's this:
It'd be nice to be able to keep the "pinned" end in place better. There is likely some other clever rigging that does it better!