This is simply semantics. She was clearly given tons of property, real estate, airplanes, vehicles and means to access goods&services only because she was the queen; including the very estate she passed away in: Balmoral Castle.
She was rich because she was part of the royal family; it's not the case that she was part of the royal family and then independent of that had private wealth. There was never a possibility of her being poor as long as she was the queen.
Balmoral Castle is owned by the family, not the Crown unlike other residences like Buckingham Palace. She was head of state. It's not uncommon for heads of state to have houses, cars, planes etc. for their use as part of the job provided by the government. Even for ceremonial ones. Should she have entertained other world leaders in a one room flat?
It was literally her job as head of state. That's part of what heads of state do. Now, being antimonarchist is a fine thing - I'm one - but not having an understanding of the duties of a head of state, elected or not, is a whole other thing.
She was rich because she was part of the royal family; it's not the case that she was part of the royal family and then independent of that had private wealth. There was never a possibility of her being poor as long as she was the queen.