Does "smug" imply anything about correctness?

My local dictionary supplies this definition:

having or showing an excessive pride in oneself or one's achievements

I was recently told by someone that, "It is only 'smug' if it isn't literally true."

We had a lengthy argument but the dictionary definition above didn't clear it up for us since it doesn't talk about correctness. Can someone say something correct or literally true but still be smug about it?

Smug is an attitude; correctness has nothing to do with it:

"the smug look of a toad breakfasting on fat marsh flies” ( William Pearson)

AHED's definition, which mentions nothing of correctness:

smug, adj.: Exhibiting or feeling great or offensive satisfaction with oneself or with one's situation; self-righteously complacent

Your dictionary is correct. Your friend isn't. You should smugly show him the dictionary.

Smug not only does not imply the falsity of what is boasted about but also implies its truth; otherwise there is nothing to boast about in the first place.

I would say that the definition proves you are right, since otherwise it would read something like "having or showing an excessive pride in oneself or one's fictional achievements".

Other definitions don't even mention achievements: "Exhibiting or feeling great or offensive satisfaction with oneself or with one's situation; self-righteously complacent."

Of course. I feel smug every time I've been to the gym, and it's literally true that I've been there.