Disclaimer: I do not use a "cheater line".
8-2 Indicating Line of Play
b. On the Putting Green
When the player’s ball is on the putting green, the player, his partner or either of their caddies may, before but not during the stroke, point out a line for putting, but in so doing the putting green must not be touched. A mark must not be placed anywhere to indicate a line for putting.
Shivas,
I think the problem with your argument doesn't lie as much with the word "mark" as it does with the word "place". Consider this: how can you "place" something that is not a physical, tangible object? I read the USGA as saying that you cannot take an object and "place it" (that is, set it down) anywhere to assist with the line of play.
How can you "place" a pen mark anywhere? Do you "place" words on a page when you write? How can you "place" a label or stamp on a golf ball?
Tape is different than marker. So they're not like situations. Since like situations must be treated alike, they can be treated differently.
See how easy it is?
Furthering my point, you would have to "place" directional tape on the club because it is a tangible object. But a pen mark is not "placed" on a ball.
So as you say, since like situations must be treated alike, and different situations can be treated differently, the fact that a pen mark, stamp or label are not objects and therefore cannot be "placed" means that the USGA can treat pen marks, stamps and labels differently than clubs, coins, tees, caddies, and other objects. And they do.
I don't think the intent of the USGA is to prohibit "indicating a line for putting". After all, as mentioned before, putters have alignment aids, golf balls have alignment aids, caddies are allowed to indicate a line for putting without touching the green, and are allowed to indicate proper alignment as long as they move before the player putts.
Rather, I think the intent of the USGA as reflected in Rule 8-2b is to prevent
objects or props from being used in certain ways to assist in putting. No object can touch the putting line (unless repairing damage), a caddie (object) can't intentionally tend the pin such that his foot is an aiming point for a putt, a caddie (object) can't stand behind the line during the stroke, a player (object) can't straddle the line to putt, and no object can be placed anywhere to indicate a line for putting.
Therefore, I would contend that using a "cheater line" doesn't violate the letter of the rule, nor does it violate the spirit of the rule, because again the rulebook doesn't appear to want to do away with indicating a line for putting, but rather it wants to limit where and how
objects can be used on the putting green.
Regarding the original Leith Rule #9: "No man at Holling his Ball, is to be allowed, to mark his way to the Hole with his Club, or anything else." I believe the original intent of that rule was to prevent players from creating indentations in the ground (with their club, or anything else) leading to the hole to make it easier to hole the putt.
Again, I don't use a "cheater line".