Cotyledons are green, and all green plant material has chlorophyll. How much it contributes is hard to say, but I agree that getting them under light does appear to avoid the development of spindly weak seedlings stretching for light.

As far as the warm mat, peppers do appear to benefit the most. You don't need as much heat as for germination. Unless your room is very cold (under 60F) other plants won't benefit much, even tomatoes. I use a large mat, so I tend to heat all my plants, but I try to keep to about 70F so which is a good balance for all plants. After about 4 weeks, I also remove heat altogether until I put them outside in the green house, where I use the heat mat only to prevent freezing. I am still experimenting with when and when not to use heat, so I may change how I do this, but so far this schedule seems to work well.

I've never heard that light doesn't matter until true leaves. Without light, I've never had sprouting seeds do anything but damp off because the stems continue to elongate, searching for light. I think somebody mislead you. But that's just my opinion.

Are you sure you don't mean that they don't need nutrients until they have true leaves? This is true, because the seed is still feeding the cotyledons.

"Upon breaking the surface and reaching the light, the seedling's developmental program is switched to photomorphogenesis. The cotyledons open upon contact with light (splitting the seed coat open, if still present) and become green, forming the first photosynthetic organs of the young plant." I included a link here, but don't know if I did it right. If not, look up seedling at Wikipedia.

Here is a link that might be useful: Seedlings

Live and learn. Just like gardening. ;)

smithmal is right.

Though some seeds do require light for germination... Most don't though.

From my limited experience, I'd say expose to light when seedlings erupt. I've noticed them grow better stronger and a better rate. If not spindly ones develop which I thought were good at the start but learned how detrimental it was.