Yes

It doesn't wash means I don't agree

you scrub when you wash because then whatever food or dirt there are on the dishes then that will come off

Yes, wash in/wash out dye washes out over about a few weeks some dyes last about 6 weeks. The wash in/wash out dyes are mostly made of vegetable oil so it's safer and certainly wash out :)

In photography (old silver and light development) when developing an exposure, the last thing you do is rinse, or wash the the paper to get the final exposure. So what wasn't on the paper before the rinse, or wash suddenly appeared. Thus the phase, "everything will come out in the rinse/wash"