Why do objects absorb all colors but re-emit only some, at the level of QM? An apple is red because (I've been told) it absorbs all colors except for red, which it reflects. Quantum mechanically, this would translate to: molecules in its skin absorb a spectrum of wavelengths, but spontaneously emit a different spectrum of wavelengths which is dominated by red. 

So why would the absorption spectrum be different from the emission spectrum, if they both come from electronic transition levels? 

(Feel free to stop me here if my question doesn't make sense, I'm ignorant about this)
I've heard the answer that the absorption spectrum accommodates much more light than the emission spectrum because the former is affected by (e.g.) thermal fluctations whereas the latter is more tightly limited to electronic transitions. 

If that's the case, shouldn't an ultracold apple stop being red? Do ultracold objects have colors?

I would guess not, as now the absorption spectrum = the emission spectrum. 
 A: 
this would translate to: molecules in its skin absorb a spectrum of wavelengths, but spontaneously emit a different spectrum of wavelengths which is dominated by red.

No, reflection and emission are separate processes.  You could say instead that the skin absorbs a spectrum of wavelengths, but much less in the red.  The EM energy that is not absorbed is reflected.  Reflection does not require atomic or molecular electron transitions.

So why would the absorption spectrum be different from the emission spectrum, if they both come from electronic transition levels?

It won't be.  But the apple is not emitting (visible) EM radiation, nor is it phosphorescent or fluorescent.  The visible light that is absorbed is re-emitted as IR.  The apple would have to be glowing to show the visible portion of its emission spectrum.  (And the molecules responsible for the red-dominated light reflection wouldn't survive heating to that temperature)


So is it correct to say the electron cloud of the apple absorbs a broad spectrum of wavelengths and re-emits mainly red?

In my answer, I was trying to separate the processes of scattering/reflection and molecular electron transitions (the latter being responsible for the absorption spectrum that removes non-red light preferentially).  As such, I would say the electron cloud absorbs a broad spectrum of wavelengths (with more efficiency away from red) and re-emits mainly IR.
You could say that there is a "absorption" happening even in the scattering case, but it's not a simple absorption by a single entity, followed by emission (and it doesn't create an emission spectrum).  I do not have the expertise to describe this process.  If this is the thrust of what you're interested in, you might want to ask that specific question (and point out where the similar questions are lacking).
A: Would comment but I don't have enough rep:
As a small note on absorption and emission: bear in mind other processes exist that can influence those spectra experimentally. Erbium doped fiber pumped at 980 nm kicks an electron into a higher state, from which it kicks off (I think) a phonon to relax to the metastable state where spontaneous emission at 1550 nm occurs. Yes, 1550 by itself will just be absorbed, but this is just all to say that depending on the problem you're considering you could see different absorption and emission behavior. 
