It will be up to you and your tax advisor to pick a position and develop the proof you would need in case of audit. If your company is providing an office in Texas, that certainly sounds like you are working in Texas at their convenience rather than your own, but that's only my opinion.
It sounds like you have already read the relevant tax rules, so what you are really asking is, do your specific circumstances meet the right tests. And really, no one can decide that except you, and maybe a professional tax advisor hired by you. No one on this board will go to an NY tax audit with you, if NY disagrees with your interpretation.
You will owe NY a non-resident return to report and pay NY tax on that portion of your income that is earned while you are living or working in the state, but it sounds like that will be less than 3% of your overall salary.
