A friend of mine, who has a 4-year-old boy, really struggled to get him toilet trained. And when he had to go, she'd whip the travel toilet out anywhere.... carparks, Sainsbury's liquor section, petrol stations and yes, parks.
Now the travel potty has been passed down to me, and I use it with my own child (well, I have it for her. She'll hold it for 6 hours before she'll use the travel potty.)
Now the woman shouldn't have had her son wee on the sign, and the verbal abuse was unnecessary. But I do understand the desperation a parent can have when their child is now mentally receptive to using something other than nasty nappies and the need for toilet training begins. (If this was indeed the case.)
Where we live, we have fabulous Tilgate Park, which has only two toilet stalls near the play area, and as you can imagine, they're always jammed during the summer. Then you also have the parents who bring everything but the kitchen sink with them when they go out, so there's less room in the toilets then what there really could be.
If we were at a park or a public area, and there was nary a public toilet in sight, my child would use the travel potty in public instead of wetting her clothes. It's the only way she's going to learn.