The role played by ultrahigh frequencies of ultrashort distances in the usual derivations of the Hawking effect is discussed and criticized. The question ``would a blackhole radiate if there were a Planck scale cutoff in the rest frame of the hole\?'' is posed. Guidance is sought from Unruh's fluid-flow analogue of black-hole radiation, by taking into account the atomic nature of the fluid. Two arguments for black-hole radiation are given which assume a Planck length cutoff. One involves the response of static accelerated detectors outside the horizon, and the other involves conservation of the expectation value of the stress tensor. Neither argument is conclusive, but they do strongly suggest that, in spite of reasonable doubt about the usual derivations of black-hole radiation, a ``safe'' derivation which avoids our ignorance of ultrashort-distance physics can likely be formulated. Remaining open questions are discussed.