'Complimentary' Car Upgrade on the Simpsons Travel ad - is this right?

[RhinestoneCowgirl]

DH and I have been discussing... can any pedants help out?

I think it is - as in "with our compliments" meaning free. (Except that somewhere along the line You Do Pay).

The other - complementary - would be "in addition to, alongside, etc" which doesn't make sense in this context.

I think this often causes confusion, though.

Thanks Habbibu - that makes sense