Oh dear, Mike, you don't know much about women. "Runner's World" forums are full of posts from women upset because as soon as they start running they want to, and indeed often DO pee. Women who have ever given birth are particularly prone to these difficulties, as are post menopausal women (older men have a problem starting to pee while older women have a problem keeping from doing so). Older women in the general population will risk their health by drinking too little because they are embarrassed to have to keep seeking out loos, and I imagine older men, with a pattern of little and often peeing due to very common prostate problems do the same.
When I was reconnoitring LDWA events, one of the things I was looking out for was pubic loos and convenient bushes/walls etc where I could have a reasonably discreet pee. The Myrtle Meander was the star event for this, with about 5 public loos en route (I imagine most of them have been closed now). In the past I have been so desperate for want of a public convenience, I have peed poorly concealed behind the yews in a churchyard - aware that if seen I would not only feel embarrassed but possibly have caused terrible offence. I have walked along a main road, bursting, looking longingly at the front gardens and wondering if anyone would notice ... It is likely that the woman you saw had previously gone through agonies of mind - would that rock be big enough? Could she veer off the track to that far off clump of trees? and then it just had to happen RIGHT NOW.
Surely everyone remembers Paula Ratcliffe's famous pee during the London Marathon. If anyone ever prepared meticulously for an event it would be Ms Ratcliffe. Do you really think she drank too much beforehand?