My theory for this is that the people who have an issue with this have an ego, and it's their pride that causes the issue. Their reaction to "no poblem" is "yea no shit im not a problem. I wasn't asking if I'm a problem." They are taking the phrase very literally, and so instead of telling them that they are welcome to do what they did (which they might already believe without you saying so, and are just waiting for your confirmation), you are telling them that what they did is not a problem. "Do you think im normally a problem?" "Would it be a problem if you hadn't said otherwise?" Etc.

Again, just my theory and it's different for everyone.