If people are oiling and rinsing the pasta, they really should reconsider their practices. Cold water sounds like advice from someone living with crappy pipes.
Exactly that - it depends on where you live and what condition your water supply pipes are in.
Homes built or renovated in the last 30 years or so will likely have copper, PVC or PEX piping, but older homes might have alternative materials that are more porous or contain contaminants. Lead was a common material used for water supply piping in the 20th century, which can combine with chemicals in the water supply to make lead salts, which can be dissolved in warm enough water. That’s not the only material that can cause problems, I’m just giving an example.
In general, warmer water can hold more solvents than colder water, so by using hot water from the tap you are giving the water more of a chance to dissolve more contaminates from your piping, which ends up in your pasta water.
Again, it really depends on what your municipal water system is like and it’s age - in some places with newer piping this is a non issue. And also keep in mind that the hot water is produced inside your house, so as long as the pipes are a non toxic material from the water heater to the faucet, the issue is pretty much nil.
FWIW, I live in a first world country where the infrastructure is old and outdated. I know for a fact my home has copper pipes, but I still don’t trust my city’s water supply, so I always start with cold water.