What does it mean for an object to absorb or reflect light?

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Is it fair to say the following?

"When light shines on an object, say a green leaf, it excites electrons on the atoms of the leaf to go to higher energy levels. As the electrons fall back to lower energy levels, the atoms of the leaf emit photons with the energy E = hv where h is Planck's constant and v is the frequency of the emitted photon. The dominant wavelengths of these photons correspond to the color green in the visible light spectrum."

If the above is true, then why do we say that leaves are green because it reflects green light and absorbs everything else? Isn't it more accurate to say that leaves absorb green light? Also, if I took a leaf to a room with only red light, why does the leaf look red rather than black?

Along the same lines, is it true that electrons can only absorb photons with the exact energy needed to move electrons from one energy level to another (as in atomic absorption spectroscopy)?

 

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reflect ::= molecules do not go excited, they just oscillate and at the same time emit the reflected wave, coherent with falling one

scatter ::= molecules got excited, but in a very short time they re-emit the light of the same wave (not-coherent with falling one) in random direction, returning 100% of the energy they got a moment before

absorb ::== molecules got excited by falling light then do something else with absorbed energy: just dissipate it thermally, use for photosynthesis...