I can tell you that in my local jurisdiction the threat was "let us search the car or we're going to hold you here until we can locate the drug dog, which is at least an hour away"...The Annoyed Man wrote: Is it legal in Texas for an LEO to threaten a homeowner with destruction of his property and killing of his pets if they have to come back with a warrant? I actually have a dog in this fight, so to speak.
Not quite the same, but obviously it's a little cohersive.
I should mention that this experience was the one exception in about 10 years and not the rule.
I caved and let the search. I found out later that courts have ruled on how long they can hold people "reasonably" during a traffic stop.
They can say anything they want.... I agree with above, get it on camera and then discuss it with their department or local media.
Honestly, if they're chasing a felon and they saw that person enter my house, I'm letting them in.