No. Light, UL, SUL, XUL has nothing to do with where you get gear. While it is true that REI or EMS or similar places carry some light weight gear, the majority of available options at those places make UL fairly incidental.
Example: A true specialty store would have a variety of stoves weighing less than 4oz running on a variety of fuels. REI for example does not carry a penny stove, or, a white box stove or a gram cracker stove. They do not carry a Caldera Cone. They do not carry a 10-12 stove. Nor can you buy alchohol fuel from them. The would much rather you spend ~$5 a pop for a canister for a weekend outing, knowing no one is ever in danger if the stove breaks. Clothing is what they really like to sell you. Why is that? It likely has a lot to do with a large profit margin and they can reinforce "style" changes. The bears don't care about style. An old down jacket works about as well as it did 10 years ago. Not what they want to hear. They would rather sell you a new jacket every other year.
UL backpacker to a regular backpacker is a lot like a fly fisherman to a regular fisherman. The stress is on skill and knowledge. Not on gear. A 3oz packet of feathers and a few sizes of hooks lets you tie most flies as you go. Why would you spend hundreds of dollars on lures? A 5 cent hook and 10 cents worth of thread and feathers will do as well as an 8 dollar lure in most cases. The skill is in knowing what to tie and how to tie it. The skill is knowing how to cast and present a fly or nymph or streamer to the fish.
Does this mean gear is unimportant? No. I UL backpacker still likes his gear. He usually has some good stuff, because he has fewer items. He will spend $400-500 on a good bag because he likes the weight. NOT because he likes the warmth. There are a LOT of bags that are warm at 20F, and a lot that are less dollars. He can often offset part of the price with a less expensive gear elswhere. A typical UL pack (say a Gossamer Gear Gorilla) goes for about $200. A typical Deuter backpack will cost ~300.
A full tent will cost around $300(or more,) a simple UL tarp costs less than $75. A simple soda can stove costs 10 cents, a Caffin canister stove costs over $150. The point is, with the skill set to go ultra light, gear essentals become easily identified and allows you to get better gear and be MORE comfortable in the woods than a regular backpacker. But, the UL gear will typically require some skill with it's use.
Once these skils are developed, it is hard to imagine a 20pound base weight being comfortable. You go to REI and find nothing that will improve on sub 10 pound. And, you start looking at technique, skills, and methodology. I never consider myself as a UL backpacker. I tried for many years to hit that goal. About 9-10 years ago I decided to weigh stuff, again. WOW. I was at 9 pounds! I have lightened up more since, but I never bother checking, it varies for every trip out (depends on conditions, and activity.) It is a nice number, but I know it is not really UL. There is stuff in my pack I use once or twice per trip, usually one or two weeks. I carry spares(batteries, line, tape, etc.) I don't bother stripping this stuff out for a weekend. No, I am not a UL backpacker. Like I say, it doesn't seem important, because every trip out (at least every 3 season trip out) is UL by the numbers. But, I know they are not. I fail to follow the UL philosophy.