Searches are presumed to be unreasonable and the burden of proof to show that consent was given falls on the prosecution.
As the conditions are imposed by the individual giving consent, the officer must not claim to meet conditions imposed when he or she knows that claim to be false.
Giving permission to search is a waiver of the Fourth Amendment and such waivers are only valid when given voluntarily and it is generally not voluntary when the consent is gained through deception or coercion.
A search by conditional consent has been held to be invalid by state courts where the conditions were knowingly not met. Therefore, the intelligent thing to do would be to obtain a warrant.
As for the last question, a search undertaken by consent is generally revocable at any time for any reason and upon revocation the search must stop unless during the search probable cause has developed. A forcible removal would complicate things a bit though.
I've taken all your comments on board, and I'm not buying them because:
A. The declarant stated with quite particularity (though it's probably FBI copy pasta) the nature and significance of an IP address. The use of "a Mac address" vs "the MAC address X" is not meaningless in a legal declaration.
B. No statements were made that the MAC address of the device seized matched the MAC address in the logs. There is nothing in the affidavit that furthers a claim that they took Y device because it had X MAC address which showed the NIC was manufactured by Apple and thus probably belonged to an Apple computer.
C. The declarant has a pretty decent command of English grammar and punctuation, but the comma placement in the paragraph isn't correct.
"Wouldn't that be something to bring up to that professor and his supervisors? That is, if they will actually listen."
Nah, once you find law that supports you, it's time to go straight to their general counsel and say: "It's either give me what I want now or have a court tell you to give me what I want AND pay me a few thousand later, your choice."
As the watches were made outside of the United States, the Ninth Circuit ruled that the watches are not covered under the right of first sale because the right of first sale only covers items lawfully made under the Copyright Act (i.e. the Ninth Circuit says that the Copyright Act right of first sale protection applies to those items made within the United States OR imported into the US with permission of the copyright holder).
Since there is a copyrighted insignia on the watch protected under US copyright law, and since the SCOTUS and Ninth Circuit says that Costco has no right to resell the item, this means that Omega can allege copyright infringement on the basis of unlawful distribution.