Honestly, not the worse advice.

No-one is going to kill themselves with a full cup of tea, they'mm most likely at least wait until drinking it.

But most people who commit suicide do it out of a temporary urge, and waiting for the coffee to cool down before drinking it and killing themselves might let the urge subside.

Sure, they're still depressed and might likely get snother urge again, but at least they live to fight another urge, instead of just killing themselves on the spot.

Not the best advice, but much better than nothing.