You say, "praising the English of someone who speaks with an accent is a harmless compliment".

Everybody speaks with an accent; native speakers of English are not restricted to the USA (where, as elsewhere, the English accent changes every few miles). English is spoken in many different ways. Why, those unaccustomed to Britain’s distinct regional accents and idiom might think that someone from London's east end and someone from Liverpool speak completely different languages! English is spoken in many countries of the Caribbean, Africa and Asia. As in the US, Britain or Ireland, it is spoken with accents, intonation and idiom particular to the culture and history of the place.

So "praising the English of someone who speaks with an accent" is tantamount to saying that someone who speaks in a different accent from yours cannot possibly be a native English speaker. At best this is ignorance, at worst, prejudice.