Yes they do supply it. I purchase it and then I can expense the device for reimbursement. There is a limit ($1500) that I can expense and once I do it I don't have the option of expensing another one for several years. I don't mind paying a little more out of pocket for a laptop that will last me. Its just been so long since I've used a dedicated Windows maching I'm a little lost.
I've read around in here and tons of other places and I think I'm narrowing it down to either Dell or Lenovo. MY IT department also just said to make sure it had some basic specs regarding processor, memory, and drive space but weren't really specific beyond that.
You mentioned you would edit 4K videos on your laptop? In this case, you may consider whether a dedicated GPU would be required or useful. If you make use of software that benefits from a GPU, then you should consider it. Otherwise, I would pick up a model with an integrated video card, as it tends to be cheaper, lighter, and have better battery life.
I suppose Dell and Lenovo are the companies that offer the best enterprise support. Perhaps HP as well. I do have an LG Gram 17 which I find excellent; it is very light and convenient despite having a 17-inch display. I could find nothing else like it. However, it does not have a dedicated GPU and I guess it is not focused on businesses.
Each of Dell and Lenovo has a line of laptops dedicated to businesses. Lenovo has its world-famous ThinkPad line, which is very good. Dell has the Latitude line for office work and the Precision line formed by workstations. I think the top-range laptops of the Dell Latitude line feel more premium than the Lenovo ThinkPads, but that may be just my impression. The Dell Latitude laptops are a little bit on the heavy side, but solid. I also found them to have better construction than the Dell XPS (which is fancy but not particularly solid).