The main thesis of this paper is that minisuperspace quantum cosmology reproduces the observer dependence of the vacuum found in quantum field theory in curved spacetime. We show that the vacua picked up by the Hartle-Hawking "no boundary" proposal in two different minisuperspaces sharing the same classical limit ($k=0$ and $k=1$ de Sitter minisuperspaces) are nonequivalent. A closer inspection suggests that the observer dependence is introduced through the choice of the Wick rotation. This hypothesis is supported by the analysis of the static de Sitter minisuperspace, where two different Euclidean sections are available, and where again two inequivalent vacua are obtained. These examples are not conclusive, but point to the possibility of a similar ambiguity even in full quantum cosmology.