You don't need a permit to buy equipment, but part of the certification course is learning the equipment, it's purpose and safe operation. There are so many brands and pieces of equipment, and you want to have the correct equipment for the type of diving you do, and equipment that fits properly, is weighted properly for your size and build, is easy for you to operate, and correct instruction in it's use, etc.
For instance, I'm prone to bronchitis when diving, because the air in the tanks is dry. I now have a regulator that recycles the moisture from exhaling back into the air I breath, and it's designed for cold water diving (which is what I do most). No more broncitis. Not everyone needs this, and it's more expensive than a basic regulator.
You do need a permit to dive.
US dive shops can lose their license if they refill dive tanks for an uncertified diver.
Dive tanks have to be inspected and current to get refills.
International dive shops certified by PADI or NAUI fall under the same rules
The most important factor in diving (other than breathing) is learning the dive tables to know your dive status, safety stops, how long you can safetly stay down.
There are so many safety factors, that diving w/o certification, is dangerous in ways you can't imagine.
And you won't have that knowledge unless you become certified.
I also suggest that you purchase DAN insurance while diving. The cost is minimal in comparison to one stay in a decompression chamber (+$10k) and it sometimes takes 2 treatments.
Authorized, licensed, reputable dive operaters WILL ask for your certs before servicing equipment, refilling tanks, or booking a dive boat, tour, or trip. A dive master on a trip will ask to see your certs before you're allowed to join the dive.