Surely it is an issue of how you define multi-collinearity.
Centering is a simple re-parameterisation that, like any
other re-parameterisation, makes no difference to the
predicted values and their standard errors (well, it will
make some small difference to the numerical computational
error, but with modern software that should be of scant
consequence). Re-parameterisation may however give
parameters that are much more interpretable, with much
reduced correlations and standard errors That is the
primary reason, if there is one, for doing it.