No, you aren’t missing anything — that scenario probably wouldn’t happen that often. 
But still, FA tracks with sessions instead of cookies, which is less than ideal, IMO. With session tracking, if the player doesn’t sign up right then and there, the affiliate is out of luck. Whereas with cookies, the player can come back days, weeks, months, or years later (in the case of Brightshare, for example), and he will still be tagged to the affiliate.