Buying and renting

I've been looking for apartments in New York City recently.  The rents are high.  This is partly due to rent control, but the prices are not very much higher than the Bay Area where I grew up.  Apparently the real estate in NYC is so expensive, even relative to the high rents, that it usually doesn't make sense to buy an apartment.  The New York Times has a handy buy/rent calculator where you can put in the price of the house, cost of rent, cost of mortgage, etc. and it will tell you how long you'd have to own a house before it paid off.  Most of the numbers I tried for the Manhattan apartments I've been curious about never pay off, i.e. it's always better to rent.    Out of curiousity, I was looking around the internet for similar prices in the Bay Area.  Since the interest rates are low now, I thought naturally it would be a better time to buy than when the rates are high.  I was surprised to find the following analysis of my mistake:

It is far better to pay a low price with a high interest rate than a high price with a low interest rate, even if the mortgage payment is the same either way.

• Your property taxes will be lower with a low purchase price.
• A low price gives you the ability to pay it all off instead of being a debt-slave for the rest of your life.
• As interest rates fall from high to low, house prices increase.
• Paying a high price now may trap you "under water", meaning you'll have a mortgage larger than the value of the house. Then you will not be able to refinance because there you'll have no equity, and will not be able to sell without a loss. Even if you get a long-term fixed rate mortgage, when rates inevitably go up the value of your property will go down. Paying a low price minimizes your damage.

 The prices are presumably lower when the interest rates are high because the demand for housing at a fixed price falls.  I'd like to see if there is really parity in the price of a mortgage for the same house at different times with different interest rates.  Does anyone know a study like this?  I'd be really surprised if the actual mortgage payments were the same.  I suppose you could use Case/Schiller and the historical interest rates to calculate the inflation-adjusted mortgage payments, but I don't have time to do it myself.