Who knows what the hell Machiavelli thought about the people having arms. First off, "the people" was probably even more exclusive than it was at the time of the American Founding. Even among the enlightened, "The People" usually means men of property or means. I doubt he even considered that a stable boy or peasant field hand ought to have a sword or a matchlock, assuming he could afford either.
And of course, 1/2 of the world who is familiar with "The Prince" thinks it's a tongue in cheek parody through hyperbole of what "The Prince" ought not to do, or was a sly critique masked by praise of what the Medici family or leaders of various Italian city-states did indeed do. At least based on Machiavelli's other works chronicling history, and his own torture and imprisonment at the hands of the government.
My gut feeling, assuming not too much has been lost in translation is that it's a mix. Both one part critique and sly parody, and one part grudging respect in the realm of the realpolitik of his day. That a Prince or leader who did not do all the "dastardly things" and manipulation would just create more war misery and chaos than the alternatives.
Although, since he seems to indicate the people would/ought to be armed either way, whatever the real reasons, I'm good with it.
IMHO, I think Machiavelli was being fairly straightforward with regards his beliefs about armed citizenry. He did believe in a militia system, of sorts. Not exactly the same as what our country's founders would use. His system would have consisted of a small cadre of officers who would maintain expertise & proficiency, and the general
"body of the people." The general populace, Machiavelli realized, had to provide for their families and in a largely agrarian society, farming was important to maintain.
Much of the ideas found in
"The Prince" would be found also in his main work,
"Discourses on Livy." I know some people think
"The Prince" is a parody, but I don't share that view; I think he saved "parody" for works like
"Mandragola" ("Mandrake Root") which seems to rival Chaucer's
"Wife of Bath" tale in ribaldness.
"The Prince" may not be a completly straightforward accounting of Machiavelli's beliefs -- it was in essence, a sort of resume; as one might prepare a resume to introduce oneself to a potential future employer,
"The Prince" was intended to ingratiate Machiavelli to a new leader. It may contain some "spin" but I personally feel he was being straightforward with his beliefs concerning an armed populace.
And, anyway, I agree with
"since he seems to indicate the people would/ought to be armed either way, whatever the real reasons, I'm good with it." 
