In minecraft, how does armor and the unbreaking enchantment work, specifically?

Now, having unbreaking 32767 would suggest that the boots would probably never break in my lifetime

is incorrect.

How Durability works:

For armor, (60 + (40/(Level+1)))% chance a use reduces durability (each durability hit against "unbreaking" armor has a 20%/27%/30% chance of being ignored). On average, armor lasts 25%/36%/43% longer.

from Minecraft wiki

Therefore, no matter how high your Durability level is, the percentage of losing one durability point must be over 60%. Specifically, with Unbreaking 32767, the chance to reduce one durability point is approximately 60.0012207%.

Just for reference, Fire Resistance, Blast Resistance, Projectile Protection and Feather Falling will not affect durability point loss.

As mentioned by SpiceWeasel in his comment, using the {Unbreakable:1} tag when summoning an item will make that piece of gear completely immune to damage. Refer to the NBT tags page for more information.