Having no debt,
This is the only part the credit reporting agency sees. In that situation they have to make the lending score base on your history, which tells them nothing of your current situation.
lots of savings, and decent income apparently counts for nothing.
The credit reporting agencies don’t see any of this. There is no component in a credit score for your savings or income.
Sure, the credit agency doesn’t see it, but the person I’m talking to at the bank to get a loan can see it when I show it to them. But it doesn’t matter and they only really seem to care about the credit score.
My guess is that the bank may start with the credit score, and if its below a threshold the bank is willing to lend to, then they don’t look any further. Unless you have a truly egregious credit history, you’ll likely find other lenders more interested in your business.
Most companies don’t want every customer. There are those that only want the safest customers because they have the lowest risk, and that may mean you might get declined even if you would otherwise have the means to service the debt.