Now, whether I could -for example- replace the HDD in that machine and try to install Windows 10, that I don't know. The hash is indeed for the machine you upgraded with all hardware it had at that point. However, for many machines upgrading is not somethiing that will happen (think laptops). I had planned to try such a situation (upgrade with 4GB RAM, nuke, install 8GB RAM and then install a fresh 10 and see whether it activates), but I have only limited time.
Besides, they're so desperate to see 10 adoption, they'll look a lot though the fingers.
What really happens is that a hardware hash is sent to Microsoft during the upgrade process. This hardware hash allows you to use those generic keys in the future (well, depending whether you had Home or Pro... Obviously), which means you can just use the generic ISO Microsoft provides (Finally, an official re-installation ISO! I've been waiting years for that). You can not use those generic keys on non-hashed hardware (Yes, I tried to see what happens). It will not activate.
However, your 7 license will remain fully functional. At least, that's my experience.
What would be an interesting test would be the following: Install Windows 7 in a VM, clone it, but don't run the second instance. Start the first instance, upgrade to 10. Keep it on 10. Now launch the second instance, which is 7 and never upgrade it. See if both remain active. This definitely violates the Microsoft licenses you have, but it would be interesting to see what happens. My prediction: both stay activated, but I'm not sure. I haven't tested it.
That is quite a lot of work, well mostly quite a lot of time, but that way I have the license, and I can continue to use whatever I like (7 or Linux), while keeping my options in the future open.
Basically, the best way is to upgrade and then rollback. That secures your "free" upgrade and you can continue to use whatever you like.
I don't dumpster dive much more these days, it's not worth the effort.
The trouble with doing something right the first time is that nobody appreciates how difficult it was.