Anything near Path (or along those illegal van routes in West New York for that matter) is not cheaper, just slightly nicer (newer and bigger) than comparable lower priced Manhattan apartments. The parent could not have been talking about that though:

Sure, rent is expensive. That's about it, and even then if you're willing to live in the right part of Jersey you can still be 30 minutes from work and have very cheap rent.

Very cheap rent is not available until your commute gets well outside of 1 hour on a good day. Which means an hour and a half on a real day. The bus/non-Path rail system is an abomination. The wait times are unpredictable, the buses regularly miss their scheduled route (meaning you wait an hour for the next one), and the drivers hate and routinely abuse the passengers.

If you want a specific example, I've lived in Teaneck NJ for under a year. People like to say that it's 15 minutes from NYC - which is true, if you have a car and make the drive at 1am on a Tuesday (plus you have to figure in around $30 for parking). At a reasonable hour and no car, it takes an hour and a half, plus the bus wait time. And Teaneck is not cheap, merely cheaper than NYC. But you still won't find much under a $1,500 a month. Of course, you must add the monthly bus pass at ~$150.