She dances around Kaylee, simplifying phrases that take her addled brain hours to concoct. She is not crazy.
River is not crazy.
She just has trouble wrapping her head around things-
So she goes to Kaylee, who is kind and organic and who speaks in terms she understands. She slips into the mechanic's mind and finds herself to be in the ship
(part of the ship); she knows it's her rightful place, crawling among wires and engines. She speaks the language of Serenity, knows its creaks and hums.
And, after all, River does feel a sort of vague responsibility for her. Somewhere in her body (perhaps in a finger or toe, somewhere small and easy to push away) she knows that her name is connected with the neatly patched scar on Kaylee's belly.
The first time they play jacks, she lets the mechanic win.