If by "streaming," you mean "having my web browser create temporary copies of media from an online source so that I can view it," then Canadian law is unclear. I can't really do better to demonstrate than to cite a few articles on the subject.
According to Alex Buonassisi and Jennifer Marles of IP law firm Oyen Wiggs:
[...] it is not entirely clear that receiving an unauthorized stream of a copyrighted work in Canada does not infringe copyright. At best, this activity could be said to fall within a grey zone.
According to Sandy Kang writing for law school blog IP Osgoode:
As for users of such websites, it is currently uncertain whether their act of streaming video would be found to infringe.
According to Michael Geist, a University of Ottawa law professor specializing in IP:
The most controversial sources are unauthorized streaming websites that offer free content without permission of the rights holder. [...] Those accessing the streams are unlikely to be infringing copyright, however.
As you can see, there is a variety of expert opinions on whether streaming pirated movies is an infringement. The section under debate is 30.71 on temporary reproductions, especially subsection (b):
It is not an infringement of copyright to make a reproduction of a work or other subject-matter if
(a) the reproduction forms an essential part of a technological process;
(b) the reproduction’s only purpose is to facilitate a use that is not an infringement of copyright; and
(c) the reproduction exists only for the duration of the technological process.
I don't want to duplicate what articles above have already stated, but I'd like to dive deeper into Bishop v. Stevens, [1990] 2 S.C.R. 467, cited by the first two articles as a similar case (reaffirmed in 2015 after a few rounds of statute amendments). In it the Supreme Court held that prerecorded "ephemeral" copies used to facilitate a broadcast was an infringement.
The key piece of reasoning is:
[... the broadcaster] has not established that, at the time of their enactment, the sections of the Act providing for the right to broadcast a performance must have been understood to include the right to prerecord. Even now it remains fully possible, and quite common, to broadcast live performances.
To me, there are two key differences why this logic might not directly transpose to the streaming pirated movies situation:
"Ephemeral" prerecorded copies aren't necessarily "temporary" copies within the scope of section 30.71 above, particularly subsections (a) and (c) might not strictly be met.
This case discusses the point of view of the broadcaster which is analogous to the hoster, not the end-user. While making ephemeral/temporary copies might not be strictly necessary for broadcasting, viewing online content necessarily creates at least a temporary copy on the end-user's computer.
Two other random notes:
None of the involved sections have a "reasonableness" or "should have known" clause whereas they are present in other parts of the Copyright Act. This means whether its legal should theoretically depend strictly on the facts (i.e. if it turns out to be illegal, pleading "oh I didn't know it was pirated" won't work).
Funny enough, I don't actually see anything in the law that would differentiate between streaming online pirated video and your example of something illegal being aired on TV provided its digital (presumably some part of the TV has a temporary copy too).
