How does Height play into hostile mob spawns?
I know that this question was asked a long time ago, but just thought I'd give an update and a correction for future people that read this. (please consider that things may also change in future)
Ok, so first of all, you mentioned that a Chunk is 16x16 block around the player. This is incorrect. A chunk is a section of the terrain and is nothing to do with where the player is. The chunk does not move. A chunk is a 16x16x256 (W,D,H). So for the mob spawning. The quote you gave is correct, however, does not note that it is centred around the chunk that the player is standing on. So 7 chunks in every direction from the border of the chunk you are standing in.
And now for your question :) Recently, (not sure when it started) height has become even more important for mob spawning and each chunk is split into segments. This is to reduce the amount the game has to render and does this by going up in 16 block segments starting from 1. So 17, 33, 49, etc. This is called the lc value and can be shown on the debug screen (F3). It is important for mob spawning, why? Because any segments in the chunk above the maximum segment that has anything other than air in do not get checked for spawning conditions. This therefore means that there are many less blocks to check which in theory will make your mob grinder or xp farm more efficient.
There is a fair amount more... however, I think this answers what you wanted. At least I hope it does ;) Best of luck guys.
Except for Slimes, height does not have an effect on mob spawning. Chunks are 16x256x16, and are loaded all at once. It is impossible for only part of a chunk to be loaded. So this means yes, it's possible for a mob to spawn near bedrock even if you're on the surface.
Note that this is not true for mob spawners. A mob spawner will only spawn a new mob if a player is within 16 blocks of it (calculated spherically).
The most important factors for mob spawning are the mob cap and the 128-block radius despawn sphere. The mob cap isn't relevant to this question other than the common knowledge fact that if hostile mobs fill the mob cap then no more will spawn. While mobs spawn in a 15x15 square of chunks centered on the player, they immediately despawn if they are not within 128 blocks from the nearest player, meaning mob spawning is effectively within a 128 block radius sphere around the player.
In 1.2.1, the max build height was raised from 127 to 255. This made building farms way up above the previous height limit, or just having the player AFK there, an attractive option. For example, if you built a mob farm in the sky at around y=90 and AFKed at y=200 or above over a relatively flat area, then the only mobs that would (effectively) spawn would be those in your mob farm, since your farm would be within 128 blocks but the mobs on the surface at about y=64 and below in unlit caves would be more than 128 blocks away and not affect the spawning rates. This saved a lot of tedious lighting up of areas and gave the crazy spawn rates similar to those in skyblock where mobs seems to spawn insanely fast (they had nowhere else to spawn). This concept still applies today to general purpose mob farms (not including mobs that only spawn in certain areas, such as slimes, witches, wither skeletons, etc.)
Nowadays (1.13+) to maximize rates as much as possible you want to build farms as close to y=0 as possible. In each chunk, for each x/z position, spawning depends on the topmost non-air block (from 1.8 - 1.13, this depended on subchunks and the highest non-daylight-transparent block so glass AFK platforms did not affect rates. This was changed in 1.14). The spawning base block is chosen randomly in a x/z position in the chunk and then randomly based on the max y level of non-air block, therefore building the farm as low as possible and ensuring there are only air blocks directly above spawning platforms maximizes spawning.
Source: gnembon EnderMINI video that explains 1.13 spawning changes at around 8 minutes, explanation of y level in spawning algorithm