Saltman, winner of the Silver Medal as leading amateur at St Andrews in 2005, was in the first group out at 6:32am and hit the second tee shot of the day - but also the fourth and fifth as well.
That was because his first attempt was sliced out of bounds into the tented village to the right of the fairway and, after playing partner Oliver Fisher had teed off, the 27-year-old Scot did the same with his second ball.
His third ball thankfully stayed in bounds and after finding the green with his sixth shot, he two-putted for a quadruple-bogey eight.
"I knew it was going to be a battle from the start," said Saltman, who recovered well with birdies at the third and fourth but eventually signed for an eight-over 79. "You can't miss it big here, you have to get it in play and I didn't do that today [Thursday].
"After that it was keep going down or try to fight back. I am not pleased with the score but I am always pleased with the way I try and play; I'm never going to give up and I am happy to break 80."
Asked if he had ever started a round in that fashion before, Saltman added: "No, but it's not the first time I've hit three tee shots on the same hole in the Open.
"I hit three on the 17th tee at St Andrews (in 2005) but thankfully found the first one."
Muirfield has two internal out of bounds, the other being the practice ground which borders the ninth fairway.
The R&A's executive director of rules and equipment standards David Rickman said: "The out of bounds in question was present in 2002 and while the tented village footprint is slightly different this year the out of bounds is fundamentally the same.
"Essentially we have two choices with an area like that. We would either play it as out of bounds or a TIO - temporary immovable obstruction.
"Our concern with the latter is that it gives free relief to any ball that goes in there and you would be dropping on a flattened piece of grass.
"We felt strategically on that first tee we did not like the notion of it being a TIO so from a rules point of view that's why when we looked at it - knowing what we did in 2002 - we decided not only was it consistent but it was right for it to be OB."