Gene-environment interactions have the potential to shed light on biological processes leading to disease and to improve the accuracy of epidemiological risk models. However, relatively few such interactions have yet been confirmed. In part this is because genetic markers such as tag SNPs are usually studied, rather than the causal variants themselves. Previous work has shown that this leads to substantial loss of power and increased sample size when gene and environment are independent. However, dependence between gene and environment can arise in several ways including mediation, pleiotropy, and confounding, and several examples of gene-environment interaction under gene-environment dependence have recently been published. Here we show that under gene-environment dependence, a statistical interaction can be present between a marker and environment even if there is no interaction between the causal variant and the environment. We give simple conditions under which there is no marker-environment interaction and note that they do not hold in general when there is gene-environment dependence. Furthermore, the gene-environment dependence applies to the causal variant and cannot be assessed from marker data. Gene-gene interactions are susceptible to the same problem if two causal variants are in linkage disequilibrium. In addition to existing concerns about mechanistic interpretations, we suggest further caution in reporting interactions for genetic markers.