Okay, I checked the web novel.
She says she can use healing magic: "私、癒やしの魔術が使えます!"
Rude evil guy says only the saintess can use it: "それは聖女様だけの魔術。"
In the web novel she didn't just heal the priest's injured leg, she regrew his amputated leg. That's why he's so surprised.
He later says that only the saintess can use healing magic to that level: "ところでいいかいアニス、これほどの癒やしの魔術が使えるのは『聖女』だけじゃ。"
However although only the saintess can directly heal in that way, there are others who have ways to heal minor problems: "これほどのものを直接癒やせる魔力は聖女しか持たないが、ちょっとしたものを治す程度なら他にもいなくもない。"
They tend to be magicians who can heal a little bit as well: "たいていは他の魔術のおまけ程度じゃがな。"
They tend to work at treatment facilities (clinics) so he offers to introduce her to one as a medic: "だがその能力は治療院では重宝される。では私がどこか治療院に治療師として紹介してあげよう。"
So yeah, minor healing magic is a thing, meaning the official shouldn't have flipped so instantly when she said she could heal. At least they should have tested her first. Most likely they were determined to get rid of her regardless and this was just an excuse.