The ball was deflected off course by some debris which had collected under the cloth when the table was moved to the centre of the arena on Wednesday.
Doherty fouled and left Hunter a chance, which the Englishman took to move 3-1 ahead at the interval, and 6-2 at the end of the session.
Former world champion Steve Davis said he had no doubt the incident had made a significant impact on the early stages of the match.
If I had been Ken, I would have been absolutely infuriated
BBC snooker pundit Steve Davis
"It made the difference between 2-2 and 1-3, no doubt about it," he said.
"If I had been Ken I would have been absolutely infuriated. You do not expect that sort of thing at this level."
After the end of the quarter-finals, one of the tables was removed and the other moved to the centre for the tournament's closing stages.
It is a delicate procedure, and as the table was settled into the floor of the Crucible arena, the slate joint underneath the cloth moved slightly and a few fragments of Plaster of Paris collected under the brown spot.
The World Professional Billiards and Snooker Association said they had taken action to ensure the problem did not affect Thursday night's semi-final between Mark Williams and Stephen Lee.
"Table fitters rectified the problem immediately after the session finished," said a tournament spokesman.
But a team of experts were in The Crucible on Thursday night relaying the cloth on the table.
The tables were also reclothed on Monday night after players expressed concerns over their speed.