Generally true.
But she could have played a wily game using indicative votes.
Ask the commons "do you want to oppose the negotiating order, do you demand that trade is talked first" The house would never have voted to spend 40 billion before talking trade. So by asking the right leading questions, she could have quelled dissenters without the power to force decisions through.
Which ever way they vote, she can then blame the house. And it would have been the UK stating it as a whole.
By keeping it to herself, she has unfairly been blamed for Barniers intransigence.