There is a very good chance here that you are not being given the full story by your son.
I DO feel your son's employer should have spoken to him first before dismissing him, given him a warning, but .....
That said, there is no way you should arrive for work late and then repeat that behaviour every day for a week. If you are late once you should realise you need to leave earlier / get an earlier train and not let it happen again.
I do not believe for 1 second they agreed to him being late and then let him go because of that. Not a chance.
I'm sorry to say, because it's never nice hearing negative comments about your child, but if he was ok with being late every day and not doing something about it, this speaks volumes for what he was like in the rest of his work / his attitude in general.
It's also interesting that you can't see that yourself.
No way on god's earth my children would be late for anything, and if they were, they would be profusely sorry and it wouldn't happen again, I can tell you that for free! My 20 yr daughter, home from Uni, had to be somewhere new, for training, yesterday for 9am. It meant getting 3 trains and she had to be there at 9am. She didn't get in from work until 12.30am for the past 5 nights and was still 10 minutes early for training. That's how we roll in our house!