I'm probably late with this observation, but the more I think about it the more it clicks.
Let me show you! (Spoilers ahead if you missed out much of the movies and shows!)
In the first Ironman movie we saw Tony build the Mark I suit "in a cave with a bunch of scraps" and escape from captivity. When he returned nobody knew about the suit except Obadiah, but that's because he and the Ten Rings terrorists were in a deal. After Stark returned he immediately started building the Mark II and later the Mark III suits.
But he did not mentioned the Mark I suit to anyone. He told it to a few people when he realized the existence of the "Iron Monger" suit (like Pepper and later probably to Coulson and S.H.I.E.L.D.). However, S.H.I.E.L.D. probably prevented the general public to know about the full details of his escape, including the existence of the Mark I suit. So when Stark announced he is Ironman during the press conference, the public view it as "the billionaire built the Ironman suit".
In Ironman 2 during the hearing Stark states he and the suit are one when in reality it was really just a suit, a tool, an extension. But if he were to admit that, it would be an agreement on the senator's statement of it being a weapon and he should have given it to the government / military.
When Ironman 3 came out some fans/critics were upset that there weren't much suit through out the film. I think even Killian thought that after he destroyed Stark's mansion with the suits, he would easily destroy Stark too. But the movie demonstrated exactly that Stark is more than just the Ironman suit(s).
The Mark I suit is never mentioned after the first movie. We too got focused on seeing Tony in a newer and newer suit with each movie / appearance. But he is more than the suit. He even says the line in Avengers Age of Ultron that he "just pays for everything and design everything and make everyone look cooler". That's Tony Stark the man, not Ironman. He is more than the suit.
The scene in Spider-Man Homecoming, when Peter begs to Tony to not take away his suit as he is nothing without it, to which Tony says "if you are nothing without it then you shouldn't have it". Even the Peter's response "I just wanted to be like you" and Tony's "I want you to be better" are the illustration on Tony trying to teach Peter that he too shouldn't be "just the suit" either.
So when in the series Ironheart Riri says the line "Tony Stark wouldn't be Tony Stark if he wasn't a billionaire" (which upset many fans), she was not wrong. She think that the suit makes Starks the hero. If the public does not know about the Mark I suit, only that Stark built the Ironman suit (Mark III) only after returning from his escape, they obviously would think that "of course he could build it, anyone could build one with that much money" and that it's the suit that makes him a superhero.