The fact sheet specifically says they are not "searching" or "seizing".
I now see you're referring to the FAQ in the OP, about residential inspections of legal stations. That is a different matter. That is not for pirate radio, but rather people operating radio stations in their private home. Here are the rules from the FAQ:
Q: The FCC Agent standing at my door does not have a search warrant, so I don't have to let him in, right?
A: Wrong. Search warrants are needed for entry involving criminal matters. One of the requirements as a licensee, or non-licensee subject to the Commission's Rules, is to allow inspection of your radio equipment by FCC personnel. Whether you operate an amateur station or any other radio device, your authorization from the Commission comes with the obligation to allow inspection. Even radio stations licensed under a "blanket" rule or approval, such as Citizen's Band (CB) Radio, are subject to the Commission's inspection requirement.
Q: Well then, if I am a low-power broadcaster and don't have an FCC license, they need a search warrant, right?
A: Wrong again. The FCC agents have the authority to inspect all radio equipment; even if you do not have a license, the FCC can still inspect your equipment. Section 303

of the Act gives the FCC the right to inspect all "stations required to be licensed." This language covers your low-power radio station. The FCC agents are inspecting the equipment, not searching your house.