Nice plant. M. parkinsonii flowers are described as pale yellowish, with a thin reddish brown midstripe. If you are privileged to have a copy of John Pilbeam's Mammillaria book and turn to p.213, there are two photos,the top one showing a plant with the pale yellowish flowers and the bottom one with a more pronounced reddish brown stripe SB315. If the grower was to sow many hundreds of seeds, at any one time, it would not surprise me to see some variation in flower colour or spines etc. Was this commercial grower mainly a cactus grower? Maybe they might have an original field collection number to investigate further or a least confirm to you if m. parkinsonii is what they believe it to be. I'm happy to call it m. parkinsonii.
An outside contender could be m.cadereytensis, which has a similar appearance to m. parkinsonii in growth, with slightly shorter spines and considered by some to be beneath m. parkinsonii, and generally comes with more deeply pink striped flowers in cultivation. Hope this helps. Derek.