I agree they are wrong, but for a different reason. Spock was never said to be the first Vulcan in Starfleet, but the first Vulcan to turn down an invitation to the Vulcan Science Academy and willingly choosing to enter Starfleet Academy instead. He was a mamma's boy and absolutely hated the condescending way they would speak to him like his human half was a handicap, and ed Starfleet to find his own way. Other Vulcan's likely went to a Vulcan Academy instead of Starfleet's and got their commission that way.

T'Pol was the first Vulcan in Starfleet, before it was even under the authority of the Federation. She even participated in the founding of the Federation, but you have to that she actually severed all ties to Vulcan when she ed at the time, and we all know how Vulcan's love to hold a grudge.