I don't know about all types of silk, especially embroidered silk, but I have washed plain silk with good results. Shampoo is the soap of choice for silk and, of course, hand washing. For thin silk, it's a good idea to iron while it is still damp; not sure about thicker silks.
If you Google silk fabrics, you should be able to find some authoritative information on washing.
I think the "no wash" fear comes from clothing made out of silk that has not been pre-washed. In that case, they say to not wash for fear the silk will shrink.
Silk makes gorgeous quilts. The only thing is I would use something other than silk for the backing so it does not slip and slide all over the place.