This would be akin to asking a shop owner if I'm allowed to pick a panflet from an endless stack of panflets placed on the sidewalk. If they don't want the public to pick panflets, don't put them where the public can reach'em!
Accessing a publicly available web service is not “taking liberties with things you don’t own”.
If you put a server on the public internet and I send it a message (assuming I’m not using ill-gotten credentials, etc.), anything it responds with is your problem, not mine.
Things on sidewalks are not free to take because you can touch them. Just like things in your front yard are not. Just because you can get to it, doesn’t mean it’s yours to take and act upon at will.
Not sure if you are deliberately missing the point. The convoluted example was more along the lines of "some company WANTS you to take pamphlets sitting on the ground in front of their store... but only take them while bending over and not while squatting". Also sidewalks are technically public property, while your front yard is a private property.