Nope, my house loan is 2.3% my liquid savings in FDLXX are about 5%. What you are saying is only true if your debt is incurred at the same time as your savings are accumulated. That's actually rather unlikely.
You missed the point. Most people take on debt when it's cheap (low interest) and take on savings when they have high returns (high interest). You save when interest rates are high, you buy when interest rates are low.