First off, I’m not an economist nor a financial service professional so I can only offer up my uneducated opinion.
I thought that – traditionally – Savings and Loans, Banks, Thrifts, etc. would take the savers money and then reloan it out at a higher rate. That way they pay the saver a lower rate of return and then make their profit.
So if lending standards are tightened then they can’t lend out as much money due to fewer people qualifying. Then they would have to keep the savers rates lower than in good lending times. IMO.