My little brother is a Boy Scout, so I've attended some of the ceremonies. One thing that's always struck me is there's usually a period in which the leader of the ceremony says something along the lines of "We now ask that you join us in a moment of silence/prayer (I don't remember which), each in your own way." followed by the moment of silence.
Why couldn't the schools take the same attitude? It's not that acknowledging religion is illegal/unconstitutional, it's that "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof" (although that, of course, only applies to Congress, not the states).
I was kicked out of Boy Scouts when I was 15 when I became confident in the lack of a god, a Christian god to be specific of what I was taught as a child.
The reason I got kicked out was because I didn't want to remain silent of my lack of such a belief.
You can believe that those silences lack specific meaning all you want, I know for a fact that you need to bow down and be reverent to a higher power, or if you don't you need to keep your mouth shut in order to be and remain a Boy Scout, and that prayer was quite regular in ceremonies. Really really bad example you gave.
for references other than my personal ones: http://en.wikipedia.org/wiki/Boy_Scouts_of_America_membership_controversies
As for having silences in school, I personally would have a big issue in practicing these "silences" as a standard for all students in a tax funded school. No one needs to announce and practice a silence time at all, you have the right to have your personal silence time all you want, just don't practice it on my child, no matter how broad you define it.