score:9
I got the invite Sunday night, to come by not the next day, but the Monday after. It's impossible for me to request leave on such short notice, let alone how hard/expensive tickets are to find due to multiple connections. I was contemplating on saying that I'm on a overseas business trip currently, and I'll be coming back on XX/03/2018 we can do the interview then.
You can say whatever you want, the airline has no reason to doubt you - plus the cost of digging up your history is too high compared to the reward - that is, catching you in a lie.
You can simply say, "I am unavailable to travel on those days and am available on XX/03/2018". You don't have to tell them why. They probably won't even ask why, as it is reasonable to expect someone would have prior engagements.
It seems to me any legitimate employer can appreciate that travel would be a burden.
Finally, are you sure this is a legitimate business offer? Normally if you are asked to visit an employer for an interview over such a distance, the employer bears the costs of the flight.
Yes, airlines have access to a passenger's future and previous travel history - but only as far as that airline is concerned.
Airline A, only knows about your history on Airline A. They do not know of any future flights you have booked on Airline B, or your previous history with Airline B.
Even if Airline A and Airline B are on a code-share agreement, data shared between airlines is only for that specific flight and not historic.
Just to close off the topic, if the airlines are part of an interline agreement, such as OneWorld, only your status is shared between the member airlines, not your history.