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From #5357 as a separated issue. The problem in the code is here: normalize is not used in the branch of fit_intercept=False.
Proposed strategy, rielaborated from a discussion with @agramfort:
write test that would fail
add a boolean option to the helper for centering data, such that it can be used to normalize also when fit_intercept=False
use this option to pass the test
raise a deprecation warning when fit_intercept=False and normalize=True, suggesting to switch to normalize=False to obtain the same result. In 2 releases time, the behaviour with those options will be changed