The aviation minister's comment today does not carry weight in excess of the photographic, factual evidence, IMO. There are too many "loopholes" that she could be exploiting without leaving her statement technically incorrect.
The good thing, such as it is, is that the facts are almost surely going to emerge here. The CVR transcript, FDR dump, and analysis of whether there's a mechanism for the electric trim to run even with the stab trim cutout switches in cutout and whether that can exceed the crew's ability to stop and reverse the trim setting manually will be telling. I do admit that the minister has greater access to that information than you or I do at this time. It is possible, but not decided, that she's had time to review all that information, knows with certainty the crew is blameless, and has chosen to not make a specific enough statement to support that for any number of valid reasons.