Nothing specifically in the rules prohibits running in a circle, or even back and forth, and for a high jump I'm not sure I would argue that much. For a long jump, I'd argue it has to be roughly in the same direction. Two additional comments, though:
- Grydan, I think your calculations are a little off, but for a slightly different reason. To attack someone you need to be in an adjacent square. From a 3D "voxel" perspective, down 1 and to the side is okay, so the PC merely needs to clear 15ft (3 squares) with his feet (else he's not in the square). This requires a check DC (with "running") of 75. At what height of clearing does the PC count to be in the adjacent square? Note that a grab is an attack and therefore there are restrictions on where you can attack from. Thinking horizontally, you can't "lunge" from two squares away, so I don't think this should be allowed vertically either. Alternatively, you just need to figure how much above 20ft is necessary for a grab attack. Is 1ft enough? Therefore, 21ft-10ft (height+reach) = 11ft, and therefore the check DC is a measly 55. I wouldn't say that reaching exactly 20ft is sufficient.
- A quirk in the rules strongly favors not recording your height, especially for small PCs. It's absolutely ridiculous, but there it is. If you don't record your height, small and medium creatures simply use 10ft for the combination of height + reach. This would imply that all small and medium creatures are about 7.5ft tall.
* Of course, the height range listed is not a hard limit, merely the suggested average range. There's actually no rule that I am aware of that restricts you from saying that your halfling is, in fact, a 7' 6" tall small creature. Good luck convincing your DM, though.
I don't really know any other 4e DM's, so my questions are these: per the RAW, can a PC even do the circle run thing to make a running jump in virtually all circumstances, and if this is technically legal per the RAW, does it feel gamey to anybody else, or am I just being a stick in the mud?
To be honest, I don't recall who came up with the wall running explanation but it sounded cool, and certainly followed the "Rule of Cool" so I was fine with the explanation.
You do make a good point though about asking the players to come up with an explanation. This is good if for no other reason than to encourage players to think outside the box rather than just "athletics". I'm not sure though I mind providing the explanation if it seems obvious to me, but in those cases, I will make sure I tell the players what that explanation is so that they understand the ruling.
As for Athletics vs. Acrobatics, I think this is one of the areas where those two skills overlap and I could certainly see an argument for either skill.
That's my point, though. In the OP, it seems like the players just want to reach something, because that's easier, but I think clearly from a rules perspective the PC wants to attack (Specifically, Grab), and therefore any rules applying to grabbing or attacking cannot be violated.While you may need to be in an adjacent square to attack someone, the rules specifically refer to Reaching Something.