Endurance athletes certainly do get gout, but that is not to say that exercise causes gout. You just need to be aware of the issues.
The first thing that is vital is to keep measuring uric acid in your blood. Exercise can affect this in different ways. Most reports that I have looked at seem to suggest an increase during exercise, with a fall to lower levels when not exercising and rested. I'll try and summarize some specific investigations to get a clearer overall picture. However, the only view that matters is your own personal uric acid level.
I copied your question into the search box in my menubar at the top of the page. It shows a few discussions about exercise and gout, but nothing much on the main reference site, so I made a start.
Thank you for your kind comments, and for prompting me to write an article about Gout & Exercise.
P.S. please go back to ER and shoot whoever said you were too healthy to get gout - or at least persuade them to join in here, where our collective minds can educate them.