It's probably a mistake to take anything Dave Arneson says at face value, the same as it's a mistake to do so with what Gary Gygax says. Like it as not, they'll distort the facts through their perceptions of the events.
Orcs, Hobbits and Elves from LotR are big influences, certainly. But so are the Harold Shea stories (by Sprague De Camp and Pratt), and the Barsoom books (by E.R.Burroughs) and other sources.
Given that
www.castleblackmoor.com (the Arneson website) incorrectly lists TSR as having the rights to the LotR rpg (they've never held it, if my facts are straight), it doesn't instill great confidence in me.
Iron Crown Enterprises held it from 1982-1999, Decipher Inc. currently holds the licence.
Perhaps the website's maintainer is mistaking the Star Wars RPG rights with the LotR rights? He's changed the original entry from what it was on the basis of an e-mail from me, but it's still wrong.
That said, I've the greatest respect for what Arneson and Gygax have done. There are probably some parallels between this and the work of Leibnitz and Newton, but I think they're fairly weak.
Cheers!