I cannot answer this for myself, but here are the experts on this subject:

Dave Ramsey answered this question on his show recently, listen here.
Summary: Risk and taxes will eat up any gains you may get through this mortgage arbitrage.

CNN Money column: Betting your home against Wall Street
Summary: Might work, given a LONG time and near-perfect market conditions. Too risky for the CNN expert.

Now, let's look at what I think people REALLY mean when they say not to pay off your house early:

Here is a quote from an article by Kimberly Lankford

Paying off your house early can help your financial situation, especially if you're nearing retirement age. But make sure the rest of your finances are in order before you devote any extra money to increase your mortgage payments, especially if you have a low interest rate. First pay off high-interest credit-card debts, save three to six months of living expenses in a liquid emergency fund, and max out your 401(k), especially if you have an employer match.

If you still have credit card debt, PAY IT OFF!
If you have no emergency fund, START SAVING!
If you are not saving for retirement at something like 15%, DO IT!
If you have children and are not saving for their college, SOCK MONEY AWAY!
Then go pay early on your house. Since the average person on the street has no savings at all, telling them not to pay extra on their house is probably good advice, as long as you don't forget to tell them to get out of debt and save for emergencies.