I believe it was independent reinvention, because the paper by Poul-Henning Kamp and Robert Watson regarding FreeBSD Jails, which was presented at a conference in 2000, says
"The jail facility has already seen widespread deployment in particular as a vehicle for delivering "virtual private server" services."
I'm not sure who that would have been. The crowds I ran with (Defcon, Blackhat, Hope) and the crowds I advertised with (k5, Slashdot) had never seen a "VPS" service before, and at no point in 2001 did we have any competition.
As I said, we struggled to even name it, settling on calling it a "server instance", and only later did we see others referring to them as "virtual private servers".
I will say that as I did my (lame, cursory) market analysis in sept/oct 2001, I did see some bizarro product from Verio where (IIRC) they were renting out slices of Sun e10ks that they had. It was exorbitantly expensive and I don't even remember if you got a proper root login ... but other than that, there was nothing.
"The jail facility has already seen widespread deployment in particular as a vehicle for delivering "virtual private server" services."
http://www.sane.nl/events/sane2000/papers/kamp.pdf