No, not at all. You're taxed on equity at fair market value when it vests. It's only after that when you get taxed at a lower rate on the capital gains.
This seems to say the opposite. If your employer grants you a statutory stock option, you generally don't include any amount in your gross income when you receive or exercise the option
The IRS page refers to Incentive Stock Options (ISOs) as "statutory" options. These are the "holy grail" because they allow you to avoid income tax at exercise and only pay capital gains when you sell.
ISOs have a 100k cap per year.
Further, the next line after your exceprt is "However, you may be subject to alternative minimum tax in the year you exercise an ISO", which is an income tax
https://www.irs.gov/taxtopics/tc427