A-ha ! I've got this problem too - I thought I'd made an error somewhere, as it certainly used to work OK.
I have the correct Caption/Alt-text/Description filled in on the media page, but the lightbox now pulls in the post title.
Example - using a WP gallery - the name of the POST shows at the top of each photo (and doesn't change for each of the 6 images) -
[gallery link="file" columns="6" ids="5845,5846,5847,5852,5853,5854"]
Interestingly, using the NextGEN gallery - the name of each IMAGE is displayed correctly -
(however this is not a good workaround as the NextGEN lightbox also appears underneath!)
Anyone else with a fix/workaround ?