#3 Brock Lesnar showed up in UFC while he was the Universal Champion
Brock Lesnar, despite being the WWE Universal Champion at the time, showed up at UFC 226 and confronted Daniel Cormier after the latter's successful fight. A match between Cormier and The Beast was teased, but it never took place. Brock Lesnar even wrestled a match in UFC in 2016 while he was still contracted to WWE.
WWE gave Lesnar permission to participate in the major MMA promotion, even though UFC didn't have a working relationship with the company. WWE, however, used to have a partnership deal with wrestling promotions such as New Japan Pro Wrestling that allowed WWE Superstars to compete outside the company.
After all those partnership deals ended, WWE wrestlers weren't allowed to compete or make appearances in other promotions. That rule still stands today. If AJ Styles or any other top stars wanted to show up in AEW, WWE would most likely say no.
Lesnar, on the other hand, was allowed to make an appearance for UFC while he was the Universal Champion, which was something that only Brock Lesnar could do.