Was not there so I will not armchair quarterback it, however containment and darting of an animal in this situation is not an unreasonable suggestion. What an agency does with it afterwards is another issue best adressed by the wildlife biologists however relocation to more remote areas again is not unreasonable if it appears that the cat just wondered in. With the right drugs and skill at darting this is not that hard and those who do it regurly are really good at it, this includes most fish and wild life agents, zoo vets, rehabers etc.
Frankly the reason why this matters is you have to ask yourself what will all the mushheads do next time there is a big cat in town? Will they ignore it? Will they try and catch it themsleves? I run into this sort of stupidity all the time with animals and public policy where people are ignorant or afriad of what will happen to the animal which offten just leads to making a bad situation worse or out of control.
BTW yotes taking domestic animals is really common here in AZ, see some small dogs that get attacked on those long retractable lead deals or in their back yards.