I have entered Singapore with less than a month left on my passport TWICE, one time it was noticed (at PPT control) the other time not. When questioned/admonished I simply stated, "I am only here 2 days, what do you care?" the officer shrugged and stamped my passport.
As for the subject matter, the Singapore government had nothing to do with "flagging" the rejection, it was simply BA's own system flagging it. Truth be told (but I do not take responsibility), had the guy just changed the date originally in his API submission there would have been no issue.......
Answering the other question though, several airlines. Mostly to do with having a valid residence permit for a certain country, which means I do not ever require a visa, and sometime idiot third party check-in agents (and supervisors) who do not want to budge. I especially love it when they try to council me, "You know you can be sent back because you do not have a visa". My questions follow with, "How many times have YOU been to country X" I LIVE THERE, and as you can see from my passport, I have NOT ever had a visa (at least not in that passport), and as you can see I have entered and exited XXX times over the last XX years including three days ago (or whenever). When this happens, and the above plays out, the problem generally disappears, if dealing with an extreme CYA person, then the pen and paper comes out, etc.
This can happen with Delta, when checking in at a non hub middle America passport, this can happen with BA when checking in in Edinburgh, or anywhere.