The fine isn't for entry, it's for some infraction upon entry (such as being drunk in public). You get in, then they fine you.

That said, American border guards have been known to turn back drunks coming in from Tijuana, but mostly as a favor to them (since they'd need to be arrested upon reentry due to public drunkenness). If you were in such a situation and insisted upon your admittance, however, I believe you would be let in.