I've had plastic bed liners. They work just fine, but it looks like they maybe didn't remove the rear rings and screw them back in after the bed liner was installed. Those screw in ones are designed to keep the bed liner in place, as well.
I would suggest going up to a farm store and purchase a heavy rubber stall mat (that's what they're called here). They are designed for horses to stand on if the horse stall has a concrete floor. They are very heavy, and will last for years. Also, if you throw something heavy in the back, it won't dent your bed!!!
Buona fortuna!!!