Very intuitive, although if we dig deeper there could actually be another meaning.
If we take the numbers you gave individually, we have 7-2-6-1-5. If we turn these into letters of the alphabet, we then get g-b-f-a-e, which are all letters used in musical notation. If we then arrange these letters into chords, we end up with e-g (major), and a-b-f, or f-a-b (minor). Translating these chords into proper words, we end up with egg and fab.
The first word (egg) relates to https://en.wikipedia.org/wiki/Humpty_Dumpty, which legend suggests is also the name of a cannon used during the Siege of 1648 as shown on the wiki, which would tie in with the theme of the American Revolutionary War. The second word (fab) relates to https://en.wikipedia.org/wiki/The_Beatles, who were also known as the Fab Four. Given the numeric theme of your suggestion above, we see that the numbers used are written in decimal notation, which is base-10. Using this information, if we look at The Beatles' 10th studio album, you will notice that it is called Yellow Submarine. And this ties in directly with my http://www.gamesas.com/topic/1523172-is-vault-111-built-like-a-submarine regarding the design of vault 111.
The big difference between this 'coincidence' and the ones I have posted on my threads is that this one is not likely to be incorporated into the game by the devs as an easter egg (no pun intended), whereas the other ones are.
EDIT: back on topic, QuakeCon will be awesome! Can't wait to get some new details from the many articles that will follow