ther is no " i believe it is the shops responsiability ", it is the shops responsiability. they should check the gear before they give it to use to use.
There's the ideal situation, and then there's reality. As a certified diver, you're responsible for making sure to the best of your ability that your equipment works as expected. And in an industry where it's not at all uncommon for rental gear to be old, worn and abused, it just makes good sense not to rely on the shop's own diligence for something you can easily check yourself.
When I was certified, I was taught to carefully check every piece of equipment before walking out the door. While a shop that's negligent or careless doesn't deserve your business, mistakes do happen even at the best of shops, and at the end of the day, you're the one diving the gear, not them.
When I rent, this is typically what I do:
1. Check the tank's VIS and Hydro date.
2. Examine the valve o-ring.
3. Hook up the tank to the regulator and check pressure (short fills happen). This also tests the SPG.
4. Listen for leaks around the valve or from the first/second stages/hoses.
5. Breathe the primary reg and octo.
6. Hook up the BC (checks buckles), inflator and fill up the BC/wing. Squeeze the bladder to make sure it's not leaking. Dump gas through power inflator and other dumps.
I've gotten bum rental equipment before from good shops, and if you catch this at the store, they find a replacement for you immediately. It adds maybe 5 minutes to the rental process, but is good peace of mind. Besides, while I appreciate that it's the shop's responsibility to rent good gear, it's my own responsibility to care for my safety and wellbeing, and that priority and responsibility trumps the shop's any day.