I like how on the one hand we have people talking about secret courts and the government wantonly ignoring the constitution whenever it pleases them, and then on the other hand we have arguments that a pedantic technicality will somehow prevent the government from getting what it wants.

Are you sure there is a law again making false statements to the general public? I think police lie all the time in sting operations or as undercover ops.

It's the compelling that is ostensibly unconstitutional.

I think the current US law is that lawmen can try to compel you to not discuss a subject, and try to jail you if you do, however, they cannot try to tell you to speak falsehoods about a subject.

Could a judge compel someone to give over access to the canary system, so that law enforcement would be the one falsely updating the canary? IAdefinitelyNAL, I've seen mentioned here and there that the police are allowed to lie while carrying out their investigations and duties.

Do you mean a false statement in public? Or in a court of law?