Based on holographic arguments Tanaka and Emparan et al have claimed that large localized static black holes do not exist in the one-brane Randall-Sundrum model. If such black holes are time-dependent as they propose, there are potentially significant phenomenological and theoretical consequences. We revisit the issue, arguing that their reasoning does not take into account the strongly coupled nature of the holographic theory. We claim that static black holes with smooth metrics should indeed exist in these theories, and give a simple example. However, although the existence of such solutions is relevant to exact and numerical solution searches, such static solutions might be dynamically unstable, again leading to time dependence with phenomenological consequences. We explore a plausible instability, suggested by Tanaka, analogous to that of Gregory and Laflamme, but argue that there is no reliable reason at this point to assume it must exist.