OK.
It just says "Maximum bet". It doesn't say "Maximum main bet" or "Maximum side bet" etc.
If you are playing mice dice at 6.25 and the side bet is 2.50, how much are you betting? Obviously, 8.75. The $2.50 bet is giving you the advantage of a feature within a set number of spins, so it is not "dead" money or irrelevant to the outcome. Your slot bet is 8.75 - plain and simple.
Take Carribean Stud Progressive for example....there is an optional side bet of $1. If you bet $5 on the game, and take the side bet, your total bet is $6. Same with the dollar ball on Playtech slots.
As I said, if this was the first time the OP had played an FG slot, then maybe one could make a case for consideration, but he admits he has played it before and knows about the side bet and how it affects the total bet, so ignorance is not a defence (neither is it a legal one). He indicated it was a lapse in concentration.....well, it might have been, but why should the casino bend the rules and carry the can for it? It also doesn't help that the OP is obviously an advantage player playing max bet every time. The casino would see this and know they are not just an average player, and would be less likely to accept the "genuine error" gambit.