Of course a centrefire scope will show parallax at rimfire distances. But if, as others already pointed out, you use good shooting technique and always place your head in the same position on the stock then the parallax is not an issue.
I've been using 3-9x centrefire scopes on my rimfires for years and have never had an issue. On my Valmet the rifle will print 5 shot groups in the 3's at 50 yds and I have made many hits on gophers at ranges from 3 feet to 200 yds.