Compliance Frameworks

Can a company state they are "XYZ" compliant even without an official attestation of compliance from a 3rd party auditing vendor?

For example: lets say i sell chairs online and am truthfully PCI compliant because i store/process/transmit payment card data. I actually have the attestation of compliance from a 3rd party auditing/compliance vendor. Can I also state I am HIPAA compliant as well even without that attestation? From a technical perspective, I am complying with all the HIPAA guidelines/framework requirements? …

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