It's partially true tho, they provide inferior price than other brokers using Citadel (because their contract apparently gives them a bigger kickback than most other brokers).
In practice price improvement is split between the trader and the broker right, some brokers might do 50/50 while others will be 80/20.
Yes this is true. It wouldn't qualify under the "best execution" standard, which is based on publicly displayed (lit) quotes.
But you are right that technically you could've been price improved slightly better had your broker signed a more favorable agreement with a market maker (and then passed it onto you). This would really venture into business economics though and is not related to regulation/legality.
In practice price improvement is split between the trader and the broker right, some brokers might do 50/50 while others will be 80/20.