It's plausible though doubtful that this was done to stifle free-speech.

That said it appears DHS were given ample time to give a comment and decided not to. That was their choice and it left their motives open for speculation, which the article writer took full advantage of when selecting a title. It's probably a bit of yellow journalism, but DHS could have squashed it with a comment saying they simply didn't want their copyrighted material to be associated with such views.

In the article, the author tries and fails to come up with some other reasons to explain this action.

So, if the takedown was not done with the intent of silencing someone, why was it issued?

Because the uploader did not own the rights to parts of his video?

Why would the DHS be issuing takedown requests on someone else's behalf, then? I believe that it's been established that isn't even legal.

Because it's possible for the DHS to hold copyrights if someone else transfers it to them.

Somehow I think the DHS is competent enough to be aware of the http://en.wikipedia.org/wiki/Streisand_effect If this was a plot to stifle speech, it was very poorly executed.

you say that as if you have a link to a mirror of the video, if not many.. ?