Code doesn't require 4 conductors anywhere.
It requires discrete neutral and ground.
Neutral's job is to handle all return current. The neutral must serve only the hot wire(s) in its own circuit, otherwise it would be at risk of overloading. (And neutrals don't have circuit breakers, so we would never know.)
Ground's job is to be a "catch-all" for any fault current. The idea is that ground returns the fault current, which flows enough current to trip the breaker. Meanwhile it also suppresses lightning and static electricity (ESD).
But nothing says ground must be a wire. It absolutely can be the metal pipe itself. Provided the pipe is UL-listed as a NEC Chapter 3 wiring method that permits its use as ground (e.g. EMT, IMC, RMC, etc.)
My "go-to" wiring method is THHN individual wires in EMT metal conduit. I own 10 colors of wire (to distinguish circuits) and none of them are green. I just don't have call for ground wires. It's an excellent system; I use it even when I don't have to. It's "aiming higher than the minimum".
2-of-3-phases is common in apartments and NYC
When I read the title I thought ground wasn't a player and you were asking about 3-phase power. Your power source is 3-phase, not the "2-phase that's really just 1 phase with a center tap" most Americans get. New York just set that as a weird little provincial standard.
However most apartments in NYC get "2 of 3 phases", which is a little weird. It's hot-hot-neutral-ground like the rest of the country, but the phases are "at an angle" to each other. So the phase-phase voltage is weird. It's 208V instead of 240V.
Bad appliances and wiring can be found anywhere, though.
Fair chance the runs from panel to outlet are also metal conduit, which means the safety grounding should be dead-nuts perfect. However if they were able to get the wiring approved without grounding, e.g. using cables in the walls, that could be a problem.
GFCI to the rescue
Ground is meant to give "shocking" faults a speedy path back to the panel, so it results in immediate breaker trip. However ground can't be everywhere.
Technology has given us a better way to detect escaping current, called the Ground Fault Circuit Interruptor or GFCI. (also called the Residual Current Device across the pond). It compares current on the hot wire(s) and current on the neutral wire. They should be exactly equal. If they're not, current is leaking out a third path (e.g. shocking someone). So GFCI is a "silver bullet" to such safety problems in older wiring.
GFCIs exist as outlets and also as circuit breakers (and a few other formats). They are also able to protect downline wiring, so they can catch faults in the wires themselves.
Installation of GFCI is probably a good idea anywhere someone reports a shock. Any shock that doesn't kill you could have if the path to ground had been better.
