There is a big difference between running a router along a straight edge and having it completely constrained by a guide rail. But the real issue here is that cutting dados (or grooves) is also inherently different from rabbets (rebate) A dado is a 180 degree cut, meaning that you are cutting with the entire leading edge (half a circle). That means there is no danger here. Half the bit is trying to climb, the other half is under cutting, they balance each other out. The point of cutting left to right is that the rotation directing does pull the router against a straight edge. If you tried to go from the opposite side, it would pull away. This ruins your cut....but it is not a climb cut. An unrestrained router will always pull to the left (as you push it away from yourself) With a router that is held by the rods, it can't do that either.
Try widening your dado, with a second pass, by moving the straight edge the wrong way, that's a climb cut. Only part of the bit is cutting, the part that wants to grab and self-feed. This is the dangerous part. If your depth of cut is enough, the router will run away from you.
There is a lot of nuance involved here, so it is generally recommended to just stick with "the rules", because accidentally breaking them is so bad.
However there is a point to be made about chip-out, splintering, and general chaos. You can under cut all day long on plywood, particle board, MDF, etc. but "real wood" (solid wood) is not so friendly about that. There is a reason to make climb cuts, but you really need to know what you are doing.