He's right when he says that your desk location (your main office, not necessarily HQ) according to HR is what matters. That's where your withholdings go. You could maybe fight with the State of California for the refund next year, but in the meantime you'll pay taxes in the state if your paycheck says so. If your desk is in NYC, but live in CT or NJ, you'll pay taxes in two states, even if you haven't set foot in your office for months. You can try changing your residency to e.g. Texas as you say, getting assigned by HR to a new office or marked as remote, but you can bet that the original state will try everything in their book to keep some of your money.

Some states are more aggressive than others. Although you're right in general, there is actually a history of CA going aggressively after the money of residents of other states, like the screenwriter in AZ that did a lot of work for a California customer: https://ota.ca.gov/wp-content/uploads/sites/54/2019/08/18032...

There is some nuance to this. CA deliberately defines anybody who is in CA "other than for a transitory purpose" as a CA resident (for tax purposes). So if you happen to reside in TX but come to Redwood City for a couple weeks and work there, for example, CA can come after you. I am fairly certain this will happen more often once increasing numbers of people vote with their feet.