> It's a public space, not your privately-owned backyard.

If you're collecting invasive plants then you're basically doing free community service. Obviously you shouldn't uproot native plants, although picking taking fruit from them isn't harmful, nor is taking foliage when done in limited amounts.

I am personally giving them my blessing to do it, and do it boldly.

People have foraged in Central Park since it was first built. Yes foraging can cause problems, but it hasn't ruined the park, and there are benefits.