The "weirdos" cause problems for everyone
"It seems that US law has decided that certain types of "private" property are not private in respect of Free Speech rights, as they are to a certain extent public areas."
This is actually just California. Federally, well, I know locally I have not seen ANY mall allow people to set up tables.
Anyway... frankly, you Brits that are saying "tolerate religious types", please recall the US is the home of the religious nutter. Of course there's plenty of normal religious types here that would be polite, set up a table and wait for people to talk to them. But if permitted, some will use bullhorns, they'll tell people they are going to hell (not even trying to convert people, just telling them they're screwed), they will go right up to people and not go away even if told to, they will follow people right to their cars. And probably try to slap bumper stickers on them while they are driving away. I have seen people that are like "OK, thanks, I've got to go" (too polite to say "STFU"), and speed up walking a little, they are followed -- speed up more, followed -- basically they'll be jogging and the religious type is still following them talking! The problem this causes for ALL people trying to push a religion is, before long, the "weirdos" will hear somehow that the polite religious types have not been bothered in some location and will start showing up -- therefore, to avoid the weirdos malls etc. end up with a blanket ban.
Anyway.. it does sound like this mall was a bit heavy-handed, if the article is all there was to it. I do question this though -- was he and these ladies having a chat, or where they trying to walk away and he following after them? The main issue, the mall official should REALLY have STFU before saying anybody that wants to talk in the mall must fill out a form!