Pruneyard Shopping Center v. Robins
No,
PruneYard Shopping Center v. Robins concerned 5th Amendment Taking Clause jurisprudence, not the First Amendment or the right to free speech.
And it concerned the relationship between the government, in this case the state of California, and residents of that state, the private property owners, where the owners of the shopping center filed suit to challenge the constitutionality of the measure allowing students access to their property to solicit signatures for their petition:
The determination of whether a state law unlawfully infringes a landowner’s property
in violation of the taking clause requires an examination of whether the restriction on private property forces some people alone to bear public burdens which, in all fairness and justice, should be born by the public as a whole. This includes inquiring into such factors as the character of the governmental action, its economic impact, and its interference with reasonable investment-backed expectations.
PruneYard Shopping Center v. Robins | Casebriefs
Again, the rights enshrined in the Bill of Rights pertain solely to the relationship between government and those governed; where conflicts between two private parties are not subject to Constitutional restrictions.
HGTV is not a ‘government,’ it lacks the authority to exact punitive measures against individuals it seeks to silence, as a government is able to do. That is indeed the purpose of the Bill of Rights, to act as a countermeasure against the authority of the state, allowing the people to seek relief in the courts to address government overreach when one’s civil liberties are in fact violated.
This is what the owners of the PruneYard Shopping Center did, when they believed the California measure violated their 5th Amendment right to do with their private property as they saw fit.