  The argument of environment-assisted invariance (known as envariance)
implying Born's rule is widely used in models for quantum measurement to reason
that they must yield the correct statistics, specifically for linear models.
However, it has recently been shown that linear collapse models can never give
rise to Born's rule. Here, we address this apparent contradiction and point out
an inconsistency in the assumptions underlying the arguments based on
envariance. We use a construction in which the role of the measurement machine
is made explicit and show that the presence of envariance does not imply every
measurement will behave according to Born's rule. Rather, it implies that every
quantum state allows a measurement machine to be constructed, which yields
Born's rule when measuring that particular state. This resolves the paradox and
is in agreement with the recent result of objective collapse models necessarily
being non-linear.
