I don't think they think their viewers will buy it per se. The idea that universal health care is bad because it leads to terrorism is probably a bit too far fetched for anyone to accept all at once. People will merely take from this the vague message of "Universal health care is bureaucratic, and beaurocracy is bad and can lead to sneakiness!" which is technically kind of true, although in a very misleading way.
In my opinion, this should be interpreted not as people giving a completely over the top reason to not support universal health care, but instead as people using a strained excuse to discuss universal health care at all (and in a negative way) in response to a news story which is only thinly connected to it. Which is shameless in its own way, of course.