But isn't the mall privately owned? At least the shops inside would be. Do different rules apply to them compared to private homes? Afaik the sovereignty of one's own home is held in very high regard in the US, why doesn't the same apply to a private business?

Train stations, as part of the public infrastructure, are probably held to a different standard. Locking somebody out from those would present quite a constraint to that individual, so that's probably for the better.