Or, to put that another way—there are two kinds of ambassadors/diplomats:
1. People the administration is paying to go out and brown-nose foreign leaders, or those leaders’ own ambassadors/diplomats, in a combination “outbound sales” and “customer service” sort of way;
2. People who presumably have the ear of the administration, where foreign leaders want to pay to impress them in order to access the administration through them.
Whether or not you call someone who’s a friend of the president an “ambassador”, foreign leaders are going to want to treat them as an ambassador, so you may as well give them the protections that playing that role requires—even if they never normally leave the country—on the off-chance that a foreign leader either runs into them or intentionally pursues and {hires through a proxy, seduces, coerces, etc.} them.
In this second sense, “ambassador” is short for “a person a state leader is worried about the welfare and mental sanctity of, in the face of global political machinery trying to manipulate the leader by any means necessary.”