The First Amendment protects against compelled speech. While courts might gag you and prevent you from speaking, they almost never compel you to speak. Compelled speech is limited to truthful speech where the statements convey important truthful information to consumers (e.g., health warnings on cigarettes). There is no precedent for a court compelling a company or person to lie.

I agree that it will be quite interesting to see how a court reacts to the idea that a person has constructed a situation in which they must lie in order to avoid disclosing the warrant. I was also interested to learn that Apple publishes a warrant canary: https://ssl.apple.com/pr/pdf/131105reportongovinforequests3.... ("Apple has never received an order under Section 215 of the USA Patriot Act. We would expect to challenge such an order if served on us.")

There must be a line, though. I suspect it would not succeed to publish many statements each like "We have received fewer than than 1,2,3,...,100 warrants of type X this year", or, "We have never received a warrant regarding an individual whose name begins with C", striking only those that are false as warrants are received. I would guess that this would cross a line, though it's difficult for me to articulate why. Ultimately there is no court precedent for warrant canaries, so the outcome is unknown.

Dismissing them trying to exercise a different power than the one they're granted by the law as a "technicality" is a disservice to the rule of law. It's not a mere technicality, it's a fundamentally different kind of action.