If fairness to H.E.R. the version performed at the 9/11 ceremony didn't include the verse above.
And that is not entirely inappropriate as the song has a long history of verses being added/omitted by Cohen and others.* Depending on which verses are included, the song's theme of yearning for the divine in the face of loss/despair/struggle isn't entirely inappropriate for a 9/11 memorial. Sure, Cohen's original appears to be mostly about the end of a romantic relationship (in which the protagonist shares significant culpability), but some of the "broken Hallelujahs" stuff is fairly universal.
Consider some of the verses H.E.R. did include.
You say I took the name in vain
I don't even know the name
But if I did, well really, what's it to ya?
There a blaze of light in every word
It doesn't matter what you heard
The holy or the broken Hallelujah
and
Baby, I've been here before
I know this room. I've walked this floor
I used to live alone before I knew ya
Any I've seen your flag on the marble arch
But love is not a victory march
It's a cold and it's a broken Hallelujah
Add in emotional vocals and a stirring musical arrangement and I can see why it gets performed at memorial services -- even if the full lyrics are a bit "off topic". The lyrics aren't perfect for the occasion, but it doesn't seem as inappropriate to me as playing "Born in the USA" at a political campaign rally or playing REM's "The One I Love" at a wedding.
Now attempting to turn Hallelujah into a Christmas song -- especially if the lyrics are "updated" to include stuff Cohen never wrote -- is another story altogether!
*The song has an interesting history as it was relatively obscure until John Cale recorded as a part of a 1991 cover album. Cale's version is significantly different from Cohen's original version from 1984. Apparently, before recording the cover, Cale reached out to Cohen for a copy of the lyrics. Cohen sent Cale 80 different verses he had written for the song. Cale eventually settled on 5 verses for the cover (2 from the 1985 original and 3 "new" verses). Jeff Buckley ended up covering Cale's version and the rest is history.
Apparently, the University of Toronto has Cohen's archives, including all 80 verses he wrote for Hallelujah. So, maybe one day these will be released and the song can be arranged to be even more versatile. I can just imagine the following fast food commercial.
They say there was a secret sauce
That David made and it pleased the boss
But you don't really care for burgers, do ya?