I used to play competitive when I was young, we traveled around the skies with our tennis bags as carry-ons. We've never had any issues. This was the Continental days for me of course. The only thing I put in my bag were my 3 tennis racquets and put everything else to the under carriage. At least if United lost my bags, I would still be able to compete.
This aggravates me a bit because like someone mentioned above, there are way too many bags out there that should have been caught to attention before her tennis bag. All these years of flying United I've never see ANY GA stop anyone for having too large of a bag.