Not true. Within the period of autocorrelation, all variation observed is measurement variation. How can you say it has nothing to do with it?
Autocorrelation is seen and exists between sequential units.
Measurement error is seen and exists within repeated measuerments of the same unit.
If repeated measurements are difficult to obtainone can leverage any existing autocorrelation to estimate measurement error by measuring sequential units.
A hopefully trivial point: the only source of variation during a period of autocorrelation is not in practice measurement error. (in theory, based on the operational definition of autocorrelation it is) there is always some variation due to small differences in other factors (environmental, pressures, thermodynamics, etc.) between units. It's just that this variation is typically so small that it is either not detectable or it simply doesn't matter given the amount of measurement error.