Question: I've heard that hot tap water is not safe to drink--is there merit to this claim or is it just an urban myth?

The only thing I can think off is the magnesium electrode in the middle of most electric water heaters. It's there to stop the body of the water heater from rusting, decaying, etc. by using electrochemical action. But it only lasts so long.. and then the magnesium is entirely gone. That's why there is typically a warranty of only two years on most water heaters. In rural situations(well water), the magnesium can react with other chemicals in the water to produce nice smelling chemicals like hydrogen sulfide. So occasionally, you will find the magnesium rod cut out of water heaters. In a situation like that, it is possible for other chemicals to leach out. I'd like to see hard data, first. There are probably more issues with the drinking also.

I thought it goes back to the old plumbing in the UK where they had two sets of pipes: a cold water tap connected directly to the water mains for drinking water, and a second hot water tap connected to a storage tank in the attic. The problem was that the storage tank was probably contaminated and considered not safe for drinking; regulations were in place to prohibit the mixing of hot and cold water. Your house is probably not plumbed that way, so the problem no longer exists. The memory of the warning "don't drink from the hot water tap" still lingers though...