I do seem to remember the original 777 design did have the folding wingtips as an option, but wasn't taken up.
Yes, Boeing developed it as part of the 'Working Together'* framework after a request from American. The idea would be that AA would use the 777 on DC-10 sized domestic gates.
From then on, AA declined to be a launch customer of the 777, but eventually ordered it quite some time later - without winglets.
(*Incidentally, as part of WT, a certain Big Airline based in north-west Europe was very keen that the 777 have a sidestick and not a yoke.)