First of all, UL DOES NOT approve anything, they LIST products. And I think your putting a little too much faith in U/L listings as breaker panel brands such as Zinsco have caused many house fires and damage DESPITE being U/L listed. This is because Zinsco breakers have an issue where they don't always trip when they should! Another bad brand that comes to mind is Crouse Hinds- I just had to fix some melted crouse hinds breakers last week. The stabs on the breakers had melted to the bus bars and all the corrosion and oxidation caused the breaker to loose power. But remember, they were U/L listed! Go figure
You can call it whatever you like, but UL tests items to see if the item passes their safety standards. Items that meet, or exceed, their safety standards, can have the UL sticker placed on the item indicating to potential buyers that the item has been tested and it meets the UL safety standards.
If an item does not have a UL sticker, it does not mean the item is unsafe, it just means the item was either not tested by UL or it was tested but didn't pass. Therefore, because there is no UL sticker, potential buyers have no idea how safe the item is. For all you know the item could be more safe than a similar item with a UL sticker, it could be equally safe, or it may not be safe at all.
My personal thoughts about UL has no relevance in this. The UL sticker is what it is and how I personally feel about their testing service makes no difference. But, if you want to know my personal thoughts about UL, I will tell you. I look for the UL sticker on things I purchase because when I see it I know that if nothing else, the product has been tested and it meets a certain level of safety standards. Can an item with a UL sticker still cause problems? Of course it can, having a UL sticker does not guarantee you will never have a problem with it. The item may be defective right from the factory, it may have been damaged in shipping, it may have been damaged through improper handling, it may have been installed incorrectly, or it may have been asked to do something it was never designed to do.
Something to consider is, if you use items that do not have the UL sticker and your house burns down, will the insurance company pay off? Maybe they would, I don't really know, but I wouldn't want to find out the hard way.