It's not terrible advice. You're getting instant return on your money paying off the mortgage and you free up your income to invest elsewhere. In the long run it's a financial no brainer.
If you pay down a mortgage right now, this is equivalent to buying a guaranteed bond with a rate of return equal to your after-tax mortgage rate. Let's assume you are in the 25% tax bracket.
If you have a 6% mortgage, you are getting a guaranteed 4.5% return. Subtract inflation and that isn't a whole lot. If you have a 4% mortgage then your ROI is only 3%. Subtract inflation and you're basically left with nothing, there is really no reason to pay it down early.
Bear in mind also that these are 30 year rates. So if you believe inflation is going to go up much at all during the next 30 years then paying down the mortgage is a net negative return.
Note that "freeing up your income" is irrelevant. You are essentially using your savings to buy a bond that increases your monthly income by a small amount, that's all.
If the guaranteed return net of inflation were 3% or so then I'd start looking at paying it down early. But rates aren't anywhere near that high.