This is correct. When I was still in grad school and the better half was working as an engineer I pretty much got the ultimatum that we needed to get married for the tax break. We had been living together for 7 years.

But then we were both working and living in SF as engineers and I did my taxes on my own for the first time about 3 years in from graduate school. I was shocked that the penalty for being married vs. not was $3000. I immediately turned to my wife, and said, "split, and split the difference?". (She understood that I was joking.) And then I discovered that you can't fix it that way, you still get taxed at the same rate. Or did. That was 30 years ago. (We're still married, humor is important.)

But after that while working at Sandia I had a PhD friend getting married to another fresh PhD, and I did tell him, do take a look at the tax hit.