Saying that you're sorry doesn't mean it was your fault or even have legal liability (which they might), it just means that you have a heart.
Saying 'I'm sorry' does legally imply it was your fault and you are liable, legally.
I am not a lawyer, but I have read my insurance documentation where it clearly says 'Don't say 'I'm sorry' if you are in an accident because ...'.
Saying that you're sorry doesn't mean it was your fault or even have legal liability (which they might), it just means that you have a heart.