The Counter Reformation argument is an ad hominem fallacy. Catholic scholars can understand Hebrew and Greek, just as well as any non-Catholic scholars. One's worldview does not necessarily disqualify his or her scholarship.
The King James Version originally had contained the Roman Catholic apocrypha, and is ultimately a product of the Latin Vulgate. The 1611 King James Version is based primarily on the Textus Receptus, which was assembled by the Catholic Erasmus.
We can trust our Bible translations because they have so much manuscript support. The New Testament alone has much earlier and wider source attestation than any other document of antiquity. It is almost one hundred percent textually pure.
Unlike the translators of the King James Version, the scholars of today know much more about Koine Greek. Scholars have learned much about the Hebrew and Greek languages since the seventeenth century. We also have discovered thousands of manuscripts and fragments which date much closer to the timing of the apostles. Our language has also changed. Thus, we can see the need for modern translations of the Bible.