You do have to keep your eye out for versions that are translations of translations (for example, The Message version is a paraphrase, not a word-for-word or literal translation), but, from what I know, the NIV version, which seems to be the version they quoted, is pretty close to the original text.

The ESV version, which is generally considered to be closer to the original than the NIV, says basically the same thing with different phrasings:

For this reason God gave them up to dishonorable passions. For their women exchanged natural relations for those that are contrary to nature; and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error.