This is incorrect. An important case is Marsh vs Alabama. [1]
A person was distributing fliers in a 'company town.' Company towns were essentially privately owned 'towns' on privately owned property. They were told to stop and leave, they refused, and were arrested for trespass. The case eventually made its way to the Supreme Court where it was thrown out. Wiki has a pretty nice synopsis of the critical point:
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The state had attempted to analogize the town's rights to the rights of homeowners to regulate the conduct of guests in their home. The Court rejected that contention by noting that ownership "does not always mean absolute dominion". The court pointed out that the more an owner opens his property up to the public in general, the more his rights are circumscribed by the statutory and constitutional rights of those who are invited in.
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That's unlikely to matter here but it's an important nuance to the 1st Amendment. It's also important for the future because it will, sooner or later, likely end up applying to social media companies who are doing everything they can frame themselves as a digital 'public square' for speech.
[1] - https://en.wikipedia.org/wiki/Marsh_v._Alabama