As a former club tinkerer I feel I can help on this one...
One reason tour player check the lofts is that forged clubs can bend slightly after repeated use, or you lean on it a certain way, an angry slam into the bag and poof it just is not the same. A tour player is so in tune with his equipment that a 1/2 a degree move could cause a radically different shot or distance than they expected.
A friend of mine in High School loved hitting 7 irons at the local range, so much so that he had a little mark in the middle of the blade about the size of a dime. They kid was very good and hit hundreds of balls a week. One day he went to get his lofts checked and it turned out that 7 iron after thousands of swings became about 3 degrees weaker. He bent it back and all was right in the world again.
For the question you laid forth about changing a six to a seven, it could be that they are looking for a specific bounce angle that is far less then what is offered in the set. Anytime you bend and iron strong or weak it has a direct impact on the amount of bounce on the club. The bent club could provide them a more desirable ball flight for their game. I think you will often see this in longer irons, bending a 3 to a 2 iron for instance. It will make that 2 iron dig pretty hard, but for a tour player that doesn't really concern with fat shots, they may prefer a slight dig with the long irons.
They could also prefer the shape of a certain iron more than another. For instance, in college I carried two Vokey 54* wedges. One bent to 52, the other 56. For my eye there was something about that Vokey 54 and bending it two degrees strong of weak gave me a solid bounce angle for my swing and look for the eye.
Another instance where this could occur is if they take an iron out of the bag and need to bend some irons around to fill the gap. One year in college I played an entire season without an eight iron. I had a nice sawed off bleeder with the seven iron and I could also go with a nuclear drawing nine iron. Instead of going this route I could of bent the lofts closer to one another but you get the idea.
This is also an interesting story I heard several years ago when I worked in a golf store. A former multiple major winner would have his caddy go out on the range with a radio at a specific distance. The player would hit balls and have his caddy radio back the distance. From there he would bend, hit some more, radio back out to get his distance. He continued to do this throughout his entire set until he met a very specific number he felt was acceptable for each club. The kicker was he rarely had the standard 3 or 4 degree gap between his irons. Some were two, some were five, some three, some four, but he knew exactly where each one of those balls were going.