Of course I can only bring the male perspective (where is womanofsubstance when you need her?).
Kwa ninavyoelewa mimi dame is actually a very respectful formal British title that has to be bestowed by the regent, in our case Queen Elizabeth herself or an appointed representative.It is the equivalent of Sir.
For example former British Prime Minister Margaret Thatcher is a Dame and in formal addresses she is addressed as "Dame Thatcher".
So to me it is a term of endearment and respect, contrary to the perception aired by the offended lady.Unless she disapproves of British aristocracy or refuses to look at the informal slang "dame" as derived from the formal and therefore reflective of the formal, I don't see where the offense is from.