The identification of cancer stem cells in vivo and in vitro relies on specific surface markers that should allow to sort cancer cells in phenotypically distinct subpopulations. Experiments report that sorted cancer cell populations after some time tend to express again all the original markers, leading to the hypothesis of phenotypic switching, according to which cancer cells can transform stochastically into cancer stem cells. Here we explore an alternative explanation based on the hypothesis that markers are not perfect and are thus unable to identify all cancer stem cells. Our analysis is based on a mathematical model for cancer cell proliferation that takes into account phenotypic switching, imperfect markers and error in the sorting process. Our conclusion is that the observation of reversible expression of surface markers after sorting does not provide sufficient evidence in support of phenotypic switching.