"Some of these payments are applied to the principal on their loans, which increases the couple’s net worth by either building their home equity or by reducing their student debt. So that’s also savings." I don't count paying down a debt as "savings". It might be an increase in net worth but not savings. If paying down debt is considered "savings" now, then the entire USA is "saving money". But I think that not only…
Paying down debt against an appreciating asset absolutely "counts as savings". Every dollar applied against the mortgage principle is an extra dollar of net worth.
There's a significant difference in liquidity though.
Savings, net worth and other similar things should always be worked out in context.