"Do you really consider the act of stealing someone's physical property to be the same?"

In principle - absolutely.

"Uploading a video of a child dancing to a song should be prosecuted by the state, with imprisonment as a valid punishment?"

This is not an example of piracy, but of copyright violation.

In any case, copyright is worthy of a thorough analysis. Where to draw the line in such corner cases can be hard to pin down.

Should I be able to author a home movie with copyrighted background music to privately show my friends and family? I think so, under fair use and for the same reason that I can buy a cd or dvd and view it with others (who didn't personally enter into contractual stipulations by purchasing it).

Should I be able to upload it to youtube - since it's a convenient venue for sharing? If it's restricted to private, invitation only viewing, I think so. If it's exposed publicly, then, unfortunately, no.

Should I be able to profit commercially from it without royalties? Of course not.

On the other hand, say I happened to catch on video my child spontaneously reciting the Magna Carta, and this remarkable event took place in a restaurant that happend to have background music playing. Should I be able to post, share, even profit from? Maybe so. I think the intent (or lack thereof) to violate copyright, while not an absolute metric in all contexts, has merit which is selectively applicable.

It's hard to codify objective assessment of intent into law, but the underlying ethical standard is that of the explicit choice to intentionally violate the property rights of another individual by acquiring a commercially available product outside of lawful venues and apart from legally valid contractual stipulations.

Piracy, on the other hand, is - without exception - a blatant manifestation of such malicious intent.

Those who do it should know it's unethical, and any attempt to justify it is merely a rationalization - as is the attempt to whitewash the practice under ambiguity and semantic nitpickery, which is the purpose of the article at hand.