It was definitely Cedric Jones. Kraft did not suddenly pop the news to Parcells during the time of the selection. Instead, Kraft initially deferred to Parcells and said he would allow BP to take Jones. That's why Parcells was there in the first place. It was only after the Giants picked Jones that the big fight developed.
We'll never find out what the truth was as to what Parcells wanted to do. He later claimed he wanted to trade down and select a DE. Will McDonough was there and he says BP wanted to pick a DE then and there. he was overruled. i have heard accounts that the target was Regan Upshaw or Duane Clemons or even Tony Brackens who went in the second round, and some have said that Parcells wanted to take a DE and then Eddie Kennison. It's all revisionist history but I believe the first hand accounts from journalists in the room. Whomever Parcells wanted AFTER Cedric Jones was picked, well, Kraft went with Grier's choice instead.
As for Faulk, how could his potential bust-edness pre-Belichick be placed on Grier? I really don't get it.