Yup, as long as you have the keys, you can use those keys on any wallet to access your funds.
The guys who lost 70m worth of bitcoin in a landfill is because those hard drives had the wallet files on them - and they didn't create backups of the keys.
This actually happened to me, though not nearly as much. I mined bitcoin in 2010 after discovering talks of it on a phpBB forum (no idea which one). I mined for about 2 weeks, and after that time, how much ever I had (I don't remember) wasn't much, so I stopped. BTC was like $0.06 back then, so maybe I had found a handful of blocks? I didn't really get back into crypto again for about 4 years. By that time, after a cross country move, I had trashed the PC that I did mining on. I didn't have backups, it was literally something I threw away because it was a gaming machine and I didn't really think about what bitcoins future was.
So those bitcoin are likely lost forever, unless someone found my HD in a dump or something and managed to decrypted the wallet I had on there. If I had backups of those keys - I'd be able to access those funds today.
Keys are everything - and the only way you actually own your crypto is if you control the keys.