You are technically correct if you regard celibacy as strictly unmarried. What Fr. Cochini has pointed out, however, is that those who were married before ordination were required to separate and practice constancy within marriage. In any case, ordination among celibates was still the norm. The West never allowed for a married clergy that still shared bed with their wives.
The Catholic Church does in fact make allowances for married priests-—I have seen many of them in my Archdiocese-—they came over from the Episcopalian Church. I do not think the Church prohibits these priests from having intimate relations with their wives. The Orthodox Church also permits married priests.