The Lions, 29-22 down when Barrett went to the bin, were 39-29 up when he returned.
Those decisions changed the momentum of the game and were made by a quartet of South African referees Jaco Peyper, touch judges Rasta Rasivhenge and Marius van der Westhuizen and TMO Marius Jonker.
So should hometown refs get to officiate a Super Rugby semi-final?
"It's an interesting question," Boyd said.
"We shouldn't need to do that but at the end of the day, whether it's sub-conscious or it's just a style, the Kiwi referees will get used to the New Zealand style and the African referees the African style and the Aussie referees the Australian style.
"I think it'll be interesting around that space. To me, there's three clearly dominant referees in Sanzaar at the moment and I think they probably could've used all three in a slightly different way."
Boyd went on to say they were Peyper, New Zealand's Glen Jackson and Angus Gardner of Australia.
Hurricanes captain Dane Coles said after the match that Peyper was a good ref, who does a good job, but that the team saw a couple of incidents differently to him.
"They [the Lions] opened up pretty easily in the first 20 minutes; we created five or six clear, and fairly simplistic, opportunities and I think the Crusaders can do that as well," said Boyd.
"That was a physical battle, that Chiefs-Crusaders one, and he Crusaders had to get through a lot of work defensively and I'd say that they'd be out on their feet a little bit and I suppose they'll be heading to the airport to get on a plane.
"It's not a bridge too far for them but it's going to be a big challenge and probably the number of forwards in their forward pack is potentially going to stand them in reasonable stead."
The Lions, who finished first on the overall Super Rugby ladder despite avoiding Kiwi opposition all season, will now enjoy home advantage in next weekend's Super Rugby final, with the Crusaders to make the 11,500km journey to the Republic.
