Rudd's mistake was in not realising that you can get away with this sort of thing when you are in the local authority, but not in Central Govt.
Local councils are wholly unaccountable - it's one of the perks of the job - and when you only have a local press to look out for, you're home and dry, because they don't have the money or time to hold anyone to account, or risk being sued. Any scandal that breaks, and they get to hide behind the 'Council spokesman'.
If Rudd were able to do that, she would still be in her job but also the scandal would likely never have broken in the first place, or if it did, it would have been a decade or so down the line (Rotherham etc grooming scandal) with the cash savings made and again, nobody accountable.