Exactly right. I've used this same tactic to silence libs more times than I can count.
If corporations have no constitutional rights, as libs maintain then:
The FBI can raid the offices of Planned Parenthood, without a warrant, and demand their financial records, patient records, etc
Local police can wiretap SEIU's phones without a warrant, probable cause and so on.
If the NAACP wanted to express itself by having a rally in a park, publishing a letter in the paper, or other tactics the local sheriff can shut them down.
When you get the libs to concede government can't do the above, they unwittingly concede corporations have some but not all constitutional rights individuals have. And that's the current state of the law - some, not all.
Public entities can have no expectation of privacy. Public. Private. The definitions speak for themselves...
If Planned Parenthood, the SEIU, and the NAACP are all being fed from tax money, then they are PUBLIC entities and should not be afforded the protections given PRIVATE PROPERTY.