It certainly feels like it sometimes.
On the other hand, I have had this happen to me, other way around. “I have a girlfriend”. The reply to me felt more about telling the person they are not being rejected based on whatever you would reject them on. Which, let’s face it, in such an encounter means looks. Nobody deals specially well with rejection. “You’re not ugly, i’m just not on the market” seems to be kinder than a “Not interested in you”
Now, I know that “no” should just be accepted. And the anger that a “no” brings is problematic. But I have a added a “I am in a relationship/married” to guys who did appear to take ‘no’ as an answer, just to make the blow to the ego softer. And I must say I felt better hearing “I am in a relationship/married” than a simple “no”. And it’s about me. Not the person being ‘owned’ by anyone.