Your friend is correct. "down in the heels", also "down at the heels" means to be poor or impoverished.
In the past, as is the case today, the heel of a boot or shoe was made out of bits of leather stacked one on top of the other. When the heels wore down, the owner would have to replace them, and that cost money. So - in the past, as may be the case today - if you had money, you had heels, and if you didn't have money, you were "down in the heels". Literally, your boot or shoe heels were worn in or worn down; figuratively, you were poor (to poor to afford to fix your shoes).
Psst. A sign of one's character, even the degree of affluence, no matter the culture, can be deduced, it's assumed, by the type and/or state of shoes or boots a person wears.
Hope that helps.