Not true. Burnham couldn't attend the Vulcan Science Academy, because only one child from a family was allowed to attend the academy. That child was her adopted brother Spock. Burnham went to Starfleet Academy instead. I believe Spock completed studies at the Vulcan Science Academy, but opted to follow his older sister into Starfleet Academy and become a Starfleet officer. Burnham was first officer of the Shinzou.