Clarified (and conveniently ignored by you) in 32423512. Here, I'll repeat myself:
There are no hard lines in the atmosphere, just fuzzy boundaries. The effective emission temperature is the average temperature of all the individual molecules that emitted all the individual photons that escaped to space, and is dominated by the temperature in the location where most of those photons were emitted. For water, that’s the altitude where the temperature first hits 0C (for hopefully obvious reasons). That of course doesn’t preclude a minor contribution from any water vapour that does manage to reach higher altitudes.
