I don't know what your article said, but that is not exactly right. The Catholic Church considers Protestant marriages valid if they are with Baptized Christians and married acccording to Protestant rules. So, if later, a new partner (who is Catholic) wants to marry a divorced man, he must seek an annulment from his earlier (Protestant) marriage and make his case before the Tribunal and get those marriage(s) nullified. This is a lengthy process that could take a couple of years. Witnesses must testify that knew the couple before and after the marriage. Families must testify.
This happened to some people I know, and the family of the woman was highly connected within the church: thus they had all the resources to get an annulment. It surprised me too. The couple cancelled their church wedding and got married elsewhere.
I don't know what is in Newt's heart, so I can't comment. I do know that, as a politician, he broke my heart back when he resigned his seat in Congress rather than be demoted after the 1998 election when it looked like his people might remove him as Speaker. I kept wondering why he had not taken a more prominent role in the impeachment proceedings, not been more outspoken about Clinton's crimes, etc. Then it all became public. I'll never trust him again.
Newt has stated that his marriage to Callista is valid in the eyes of the Catholic church and that he is a practicing Catholic along with his wife. I assume that is the truth, as there has been nothing in the press to dispute that. The article merely stated how that possibly happened.