Yeah they like to sit on eggs... after they are done laying. Not necessarily because they are broody but because they just like to!... We have an old Leghorn who stopped laying eggs... but she loves to sit on eggs still.... The younger ladies are not very appreciative of her clucking and pushing them out of the nest boxes.
I have been around tens of 1,000s of white leghorn hens going back 70 years and in that time I have never seen, heard, or known of a white leghorn hen, sitting, clucking, incubating, brooding, or in any way acting in a mothering way. There are some white hens who will sit but they are not white leghorns or at least pure whiteleghorns, though I can't speak for all hens who may have some unknown amount of leghorn DNA.. Instead I suspect that your old hen... has lumbago and she wanted to sit down for a spell and rest her aching bones.