They played a role but things would have been more or less the same either way. Their biggest role was supplying capital for nonviable businesses. Once things began unraveling, it didn't matter anymore.
Why should a bank lend your company 25% of their payroll when (presumably) demand has fallen through the floor? That's not a rhetorical question. Unless your company was funded by an investment bank, the IBanking industry has nothing to do with your company having to go through with layoffs, other than setting up the pins for a collapse in the mortgage sector (i.e. the reason why your company couldn't get loans from a retail bank). But that doesn't mean the retail banks, homeowners, consumers, business,etc. aren't responsible for going along with the scheme. Why didn't your company save more money so that it could weather a longer & more severe recession without having to make cuts?