The identification of black holes is one of the most important tasks of modern astrophysics. Candidates have been selected among binary stars based on a high mass function, and seriously considered when the lower mass limit exceeds ∼3 M� . More recently the absence of (type I) thermonuclear bursts has been advanced as an additional criterion in favor of the black hole interpretation, since the absence of a solid surface naturally precludes the accumulation and ignition of accreting material. We discuss in this Letter the possibility that self-bound stars made of CFL-paired quarks mimic the behavior of at least the low-mass end black holes as a result of: a) higher maximum masses than ordinary neutron stars, b) low steady luminosities due to the bare surface properties, and c) impossibility of generating type I bursts because of the complete absence of normal matter crusts at their surfaces. These features caution against a positive identification of event horizons based on the lack of bursts.