is displayed with the caption "Barack Obama holds his right hand in the air as he and Michelle Obama both smile towards a balding man whose back is to the camera while a large crowd watches." It seems to me like the ALT text should be in the fallback chain after the file description, not before, as it is often written specifically for users with screen readers.
The ALT text is not used for fallback; the link title is. The wikitext format is [[File:filename.ext|frameless|title|alt=alt text]]. See example where the two are different.
The infobox template apparently uses the alt text as the title, instead of the caption; IMO that doesn't make much sense.
Left some messages about it on-wiki:
Closing this ticket as I don't see anything that could be done on the software side about this.