What seriously contributed to his death was a bullet from the ground. I think it was an american bullet. Can't say for certain. Forgot. He was struck in the head. But the bullet did not penetrate the scull. Instead he recieved a concussion. A concussion sometimes has psychological ramificiation which the pilot according to witnesses exhibited in days between that wounding and death. He seemed a little bit out of his mind, unreasonable and illogical. In this condition he took to the air. And perhaps took chances that he would not have if he was healthy.
Most modern accounts place the Aussie gunners with the downing of the Red Baron. Capt. Brown got the official credit probably because he was an officer, most likely for propoganda purposes they didn't want to credit grunts with killing such an icon of the enemy.
BTW, parachutes were invented at this time, but they were very cumbersome and looked down upon as cowardly by the chivalrously minded airmen.
I have always felt it is more than a little bit of a snub how the British use Commonwealth troops for cannonfodder, then somehow manage to get most of the glory distributed to themselves. If it were not for South Africa, Australia, New Zealand, Rhodesia (RIP, sold out by the Brits entirely) and Canada, the Brits really would be speaking German right now, regardless of the US.