Seems to me we are talking about two different uses for a compression sock. Two VERY different uses.
One is the so-called performance-enhancing idea, which has been researched and found to be false. No improvement was found at all in the controlled trials I read about.
The other is for medical reasons, and Ray has illustrated this. For medical use a compression sock can help in a couple of ways. The first is to reduce swelling. That is standard practice and part of RICE. It can help limit damage caused later.
The second use is to assist with weak arterial valves, varicose veins (which form part of DVT), damaged arteries and probably damaged ankle regions. It works as follows.
The arteries have valves in them to keep the blood flowing towards the heart. When the valves are weak or damaged, blood can flow backwards in between heart pulses. That is bad stuff. Compression around the valves can help them seal so the blood only flows forward. This is how compression helps with circulation: it helps to restore the performance of the circulation system to what it *should have been*.
Note the crucial difference here. Compression does NOT enhance blood flow at all, it just helps restore it from a damaged state back to normal correct behaviour. This is what the medicos mean when they say it 'helps': they just omit the last bit. But then, you only go to the medics when you are not healthy.
Some of the spin doctor claims may be due to their just not understanding the difference. Dare I suggest the rest are simply profit-oriented?
PS: Ray - hope that ankle heals!