The theoretical underpinning behind this idea is the Modliglani-Miller (M-M) theorem which states that if certain assumptions hold (symmetric information and rational behaviour of market participants, complete, frictionless markets etc) the funding structure of a firm is irrelevant for its business decisions. In an M-M world, the primary differences between the costs of debt and equity can stem only from their different tax treatment.
Both the paper of Miles et al (2011) and Kashyap et al (2010) are based on the – at least partial – validity of the M-M theorem. The relevant point is that more capital reduces the volatility of return on equity and increases the safety of debt thereby reducing the required returns by the market on both equity and debt.