However, there was better news for the Scots when it emerged that Euan Murray, the 59-times-capped Lions prop who ruled himself out of the summer tour for personal reasons, could yet figure in one or both of the later games against Argentina and South Africa.
Murray's situation was outlined at the team hotel by the scrum coach Massimo Cuttitta, who said he was generally happy with the way his players had performed in the set-piece in their 24-6 win against the USA last weekend.
Scotland capped two new loosehead props, Gordon Reid and Alex Allan, during the course of that game. Their experience could be vital in the forthcoming autumn Tests, for it has also been confirmed that Ryan Grant will be out of action for up to six months following shoulder surgery. The hooker Dougie Hall has also been under the knife, having an operation on his arm that will also sideline him for a lengthy period.
Hamilton and Taylor will be replaced by the Glasgow Warriors duo Tim Swinson and Peter Horne. Swinson and Horne were scheduled to join the tour for the Argentina and South Africa legs anyway, so their arrivals have effectively been brought forward by one week.
Vern Cotter, the Scotland head coach, said: "This is obviously disappointing news for both these players [Hamilton and Taylor] who were keen to impress in the short time they had on this tour. Everyone in the squad wishes them well and a quick recovery. It's now up to Peter and Tim to continue the hard work put in by Duncan and Jim, and take advantage of this opportunity, as we prepare for another Test match."
Geoff Cross, whose father passed away a few days before the USA game - the Scottish players wore black armbands as a mark of respect - is to remain with the squad for the rest of the tour. It had been expected that the prop would fly home, but Cuttitta revealed that the 31-year-old had expressed a wish to stay with his team-mates.
"There was no pressure from us," said Cuttitta. "Absolutely no pressure from the management, the coaches or anybody. We were all surprised [that he stayed]. I think it is probably his attachment to the team.
"I think it is probably what his dad would have wanted from him, but that's just my opinion. It is a delicate thing. It is his dad: an important thing in his life. He is showing a lot of affection to the national team, sacrificing something. It is a big thing."
Cuttitta refused to go into the details of Murray's situation, but said he was delighted that the player, who is currently without a club after his contract at Worcester Warriors expired, could soon be back on the pitch for Scotland again.
"He might be available, he might be coming. If we need him I think he could come out," said Cuttitta. "He had valid reasons to stay home, family reasons. I hope he is part of this group because he has a lot to offer. Every time he has gone on the field he has offered us a lot."
Mike Catt admits that England's coaching team faces the toughest of selection meetings as they finalise plans for the second Test against New Zealand. With so many players making compelling cases for their retention in Saturday's agonising 20-15 loss at Eden Park, myriad permutations have opened up as the Aviva Premiership finalists come into contention for the first time.
The identity of England's hooker, lock, blindside flanker, scrum-half, wing and inside centre will be causing Stuart Lancaster and his coaches headaches.
"We performed particularly well on the weekend," said Catt, the attacking skills coach. "It will be a tough selection because a lot of them performed admirably. Some people will be very happy and some won't because we have competition in all these positions now.
"That's the beauty of this team at the moment. It's starting to have that level of competition for places, so no-one wants to give up their shirts."