They can still do this if the old code base is under a permissive license, since permissive licenses like BSD, Apache and MIT are compatible with proprietary licenses.
The license terms for a sub-license must be consistent with the original license terms, although not necessarily the same. The sub-licensor can use different words as in the original license, but they cannot override the terms and conditions that are required by that license. The sub-licensor cannot sub-license more rights than have been granted by the original license.
Works released under the Apache, BSD, and MIT license can be included in a larger work with a more restrictive license or modifications can be put under such a restrictive license, but the original license must remain intact.
If you are getting your information on re-licensing from the Wikipedia page below, it is wrong.
They can't hide the fact that it was once MIT/BSD/Apache licensed, and they still have to include copies of that original license (and any notices) even after the switch, as that is one of the conditions that contributors make their work available under, and failure to do so would mean the org is in violation if they haven't otherwise received approval.