It's like in Miller and Modigliani's model if the firms start borrowing a lot more, but the shareholders are mostly not really paying attention, and/or don't know well the implications, so for the most part they don't borrow any less to compensate. In that case, aggregate demand for borrowing would not remain unchanged. The aggregate demand curve for borrowing would, in fact, shift out, and the interest rate would rise.
From UCLA economist Roger Farmer:
A wealth of evidence shows not just that quantitative easing matters, but also that qualitative easing matters. (see for example Krishnamurthy and Vissing-Jorgensen, Hamilton and Wu, Gagnon et al). In other words, QE works in practice but not in theory. Perhaps its time to jettison the theory.