This case will surely reach the Supreme Court of Canada.
Apparently the Mounted Police spokesperson is referring to this 1999 Supreme Court of Canada case, which on the face of it does not involve comparable circumstances.
The woman involved, who had mistakenly dialed 911 instead of 411 met officers on the front porch and while she denied them access to her private residence - as is her common law right - the attending could easily ascertain that there was nothing untoward occurring. Well, at least that's what the couple pursuing the lawsuit will contend.
The police will likely invoke the spectre of child porn and whatever other horrors might theoretically be going on in the residence in an effort to line up their actions with the reasoning laid out in the case law, including the 1999 SCC decision.
For a quickie summary of police detention powers, take a gander at this lucidity written piece.
Too bad the police didn't read this little summary provided by a law enforcement association in 2001 to British Columbia police officers.
Lawyers out there may wish to offer some insights.