The entire COC issue deals with liability for loss & damage. There is no prohibition on acceptance. An item is either acceptable for check-in, acceptable for check-in with special packaging or acceptable only with a signed release. All of the COC language is an inverse way of getting to that point.

For what it is worth, Amazon has several stroller bags which cost in the $10-15 range and which make gate-checking quite easy. The bags won't protect a stroller from large containers, but they do keep them clean.