I haven't been in the position of begging for food money (I've busked, but that was for pocket money, so and also it's not the same) so these reasons are from my imagination, not experience. As such, they likely lack nuance and I'm probably missing piles more.
I'm not even saying one should never offer a hamburger to beggars. Just, if they refuse it, that isn't evidence that they don't need the money.
- They don't know where that hamburger's been.
- They're vegetarian.
- They're gluten-free.
- Or lactose-intolerant.
- Or have other allergies.
- Or other medical conditions.
- Or just want to eat healthily to prevent future medical conditions which they won't be able to afford to treat.
- They've actually just eaten. It's just that they'd like to eat tomorrow too, but it's forecast for rain: miserable and unprofitable weather for begging, and a dollar keeps better than your hamburger.
- They've actually just eaten. It's just that they'd like to feed their kid too, and a hamburger is a poor substitute for formula.
- They lied. They don't need money for food. It's just that they don't have a card that says "Need money for toothpaste and toilet paper".
- They lied. They don't need money for food. It's just that begging for food money gets more money than begging for shoes-that-don't-leak money.
- Let alone for condom money.
- They'd love a hamburger right now. But begging for charity is soul-destroying enough at the best of times, let alone when someone implies they're a drunken gambling-addicted drug addict not to be trusted with bit of spare change. Honestly they'd rather starve for another day than accept your right to judge their sincerity.
- Bugger the burger. They've had a shitty week and they deserve a beer, dammit.
I'm not even saying one should never offer a hamburger to beggars. Just, if they refuse it, that isn't evidence that they don't need the money.