I totally disagree. It is similar in the scheme of things to telling a suspect that they failed a polygraph, or that there is a video of them when there isn't. It is an easy, "mostly legal", means to an end.
To put this in perspective just answer one question: how would LE have gotten probable cause for a search warrant in this case, otherwise?
Seriously, PC is one of the hardest things to get, and judges shoot down requests all the time. A missing baby is not enough. Holes in the mom's story is not enough. But a cadaver dog hit? Oh yeah - that's enough!