My normal usage for this type of punctuation, when not quoting, is to place them around a statement that I wish to not take responsibility for or to express contempt for the statement thusly surrounded.
However, I have seen usage of these symbols with expressions that might be taken seriously: a fifty-year-old G.I. Fathers’ Day plaque with the words 'My Dad—“The Greatest Of Them All” ', a Mel Bay guitar book that ended with the words 'End of Grade One—“Proceed To Grade Two” ', or an advertisement such as 'Here at Anytown Grocery “We’re Here To Serve You” '.
Today, these statements would seem to be quoteless, as putting them in quotes would (as least to me) make me wary of what exactly is going on; it would be a hint to search for fine print.
So, was the use of quotes many years ago not so symbolic of doubt as they seem to be today?