Tweet the shit out of it.
It's one little girl, ffs.
Right, so it's a busy park that's frequently teeming with kids, but not one of the other children has ever found themselves desperate for a wee and their parent thought "Ooh, Pizza Hut will have a toilet." ?
As other posters have said, loads of people of all ages and in all circumstances sometimes find themselves desperate for a toilet - in fact, I doubt you could find a single person who could honestly say that they've never been caught short. Nobody wants to wet or crap themselves, but it doesn't make it some random company's problem to step in and take the hit to their business.
What about if a very poor and/or homeless person found themselves outside a food establishment feeling weak with hunger but penniless to pay for any food? Yes, it would be kind if the manager did decide to offer some free, but in what world would you hurl abuse at them, let alone a junior member of staff, if they said "Sorry, you're welcome to buy food, but we sell it here - we don't give it away."
Even if they did give the needy person a free sandwich, people would see and word would get around and, before long, you'd get loads of poor folk - as well as those claiming to be poor - expecting to be given a freebie. Every one of them in the queue would individually be 'just one person'.
I think, as has already been said, most people assume that they're the only one who ever thinks to make a cheeky request or otherwise things that the rules shouldn't apply to them. A PP mentioned 'vagrants' coming in to use the toilets, by which I'm assuming the intended reading was 'undesirables'. Just because you have a home and are wearing clean clothes doesn't make you any less of an undesirable when you're seeking to cost a random business money rather than being a customer from whom they can earn a profit and keep their business going.
Also, whether a vagrant or in your best finery, there's no telling as to which people will leave a toilet clean and who will leave it an appalling mess - toilets that people don't have to clean themselves are a great leveller when it comes to the risk of a user rendering it a public health hazard.
Also, I daresay that a person identifying themselves as desperate is statistically more likely to end up making a mess than a standard case of a healthy adult realising that they will need to go soon and being in a position to take their time getting there, with no risk of not quite making it and the inevitable aftermath.
Nobody would ever admit to making a huge mess in a toilet if they knew they could get away unnoticed - whether through a lack of consideration for anybody else or just pure embarrassment - they'd just scarper. If you wouldn't in your wildest dreams find yourself passing a cafe or restaurant and thinking "I've got a spare 20 minutes - I'll go and offer to clean their toilet for them" out of kindness and love for your fellow human beings, why would you think that they should risk subjecting their cleaners and paying customers to a vile, stinking, potentially unusable toilet, caused by somebody with no relationship with their business at all?