Sure there is. On the hiring of Pruitt you act like we had choices and that Fulmer didn't walk into a search that had already hired one person and begun interviewing replacements after our very public protest of aforementioned first hire made national headlines and sent the AD into a tailspin. To say that options were limited would be the understatement of the year. Fulmer was hired to stop the bleeding which he immediately did by 1. recruiting and 2. becoming a symbol for fans to rally behind during a fragile time. The latter was his only real job the entire time. Folks forget that Fulmer's hiring as AD was meant to be temporary -- his job was to rally the troops and stabilize things which he did to a large degree. But he was never a normal AD nor was he hired to be. Fulmer was a public face and advocate for UT Sports but not the guy writing contracts and running day to day budgets (those go to vice-ADs and others anyway).
Regarding Barnes... Almost? Really, you're going with almost? Close only counts in horse shoes and hand grenades. You can't possibly blame Fulmer for Barnes considering one the best jobs in his field when that job is ALSO offering a giant paycheck. Even so, gotta credit Fulmer with the win since Barnes stayed. Surely that mitigates an almost.
Regarding Holly... Not sure what the issue was here. Holly wasn't cutting it but she wasn't as awful as we portray either - Elite 8, Sweet 16, Elite 8, Elite 8, Second Rd, Second Rd, and 1st Rd. Not good enough for the LV program but until the last few seasons not quite enough to simply cut her either. At any rate, he inherited Holly during the 2017-18 season. He was hired in December of 2017 so there was no way she was getting fired during the disaster we had on our hands when he was hired. He fired her after the 2018-2019 season. That's called doing his job pretty damned well despite the fact that Holly was a friend.
The big criticism that sticks to Phil as AD imo is the fact that he didn't distance himself from Pruitt. He's not at fault for hiring him given the circumstances but he is at fault for wanting to give him another year. I think Fulmer's own treatment by the AD blinded him when it came to Pruitt. He didn't think Pruitt would be fired (and that **** was being signaled to him by the guys who pay the buyouts and pay the next contract until the very end when something changed and it had to be a bit more than the initial NCAA stuff because that was blown off at first) and he didn't want to give Pruitt a final year with an AD that was setting him up to fail.
I think you have to grade the job taking into account that Fulmer was an interim whose main job was simply to be him in public, raise money, and calm the immediate whirlwind that had been unleashed post-Schiano. That we couldn't get our ish together long enough to replace him before Pruitt needed to be fired is on us. Fulmer was never going to make the next hire anyway and everyone (including him) knew that but we drug our heels because we couldn't find a candidate everyone could agree on without starting yet another internal war until Danny White came along.