I'm saying that using minimal means does not make an unconstitutional action acceptable; you're pointing out that using excessive means can make a constitutional action unacceptable. That's a different situation and not really a reply to my comment or this case.
To make it more relevant, can you point to a single case where a court has ruled that a constitutionally limited action was permitted simply because the means were unintrusive?
A compelling government interest, as you said, could justify the action, but what is the compelling government interest here?