Are board stiffeners OK?
When they're designed as board-stiffeners, sure. They're no problem.

On the page:


  We offer single and multi-layer copper bus bars both insulated and un-insulated. The snap-in rigid/bus stiffeners provide board rigidity without the need to clinch pins.


Critical section highlighted. 

They're not relying on the solder for mechanical support. The pins are shaped so they lock into the PCB.



It's worth noting that they also bill them as helping in high-vibration environments.

While I do agree that if you can, you should have more screw-mounting points for a PCB, I think Board-Stiffeners are more intended for situations where you are designing a system to fit into pre-existing packaging, and adding additional PCB supports is not an option. 

If your choices are "sagging PCB" and "PCB with stiffener", it's pretty obvious what the better answer is.

The answer is to fire your mechanical engineer