I'm assuming that you're referring to how Rashi explains עבודת יחיד as the second entrance of the cohen gadol to remove the כף ומחתה. (But see the Rambam, who understands that none of this has to do with Yom Kippur.) So you're making an interesting point: Apparently private individuals can only buy the clothing (and turn it over to the tzibbur) for the second entrance, but not for the first. As it says in the b'raisa,
אחר שכלתה עבודת ציבור, כהן שעשתה לו אמו כתונת לובשה ועובד בה עבודת יחיד, ובלבד שימסרנה לציבור
Sounds like for the first entrance (which Rashi would call עבודת ציבור) this would not be allowed.
So I'm having trouble reading the mishnah:
אלו משל ציבור, ואם רצה להוסיף ־ מוסיף משלו
which sounds like it applies to both.
Haven't had a chance to look at the mefarshim; maybe you did?