Yeah, Adam has told this story a few times. He was wearing his military jacket in 1980 and Michael wears one that is a low-key, simpler version at the Budweiser Superfest in 1982. He also wore it at that Liza Minnelli concert, can't remember the date.
Not that Adam started it. Jimi Hendrix, in 1967, had two military jackets that he wore.
Here's the fancy one:
It's always claimed that the jackets worn by Jimi and Adam were Royal Hussar jackets (8th & 11th Hussars). Adam's jacket apparently came from Bermans and Nathans, theatrical costumiers, so it could be legit. Jimi got his from Chelsea Antiques Market.
Sidenote: Michael was also interested in the Burundi-influenced drumming that Adam used in some of his songs in 1980.