Since I moved to Missouri, I've been upset by a similar grammatical error: quotation marks used for emphasis. You would expect, say, all-capitals or an underline or italics, but you instead see 'Come taste the "best" burger in Missouri,' which is awful.

In New York, where I grew up, that use of quotation marks is called "scare quotes": quotation marks in all cases signal that you're detaching a text fragment from its context; with scare quotes you detach a phrase which reads just fine in that context to either bring focus to the phrase (like when you're defining it) or to indicate that the phrase itself is somehow problematic (like when you want to criticize the phrase, e.g. 'these "businessmen" are stealing our money,' where you're implying that they are either not truly men or not truly doing business per se.)

When you say that you have 'the "best" burger', to me it sounds like you're implicitly adding at the end, 'well, at least, it's the best at being an awful burger.'