Tuning is arbitrary. I've listened to some comparisons between A=432 vs 440 and I think the 440 actually sounds better. But then again, like this article even states, it depends so much on the piece. If you're listening to stuff from the 1700s/1800s, it would make sense to try to use the tuning they used at the time, if only to try to get the sense of emotion intended by the originally composers/arrangers/musicians (even then it's a best guess).
But yes, it is pretty arbitrary. It's the tuning of a note depended on the number of cycles per some arbitrary time unit we defined.
If you're listening to a song today, with all our sound precision technology, you're hearing it the way the original author/musicians wanted it to sound (depending on your equalizers, speakers and various other audio setup).