Absolutely true. Several years ago I had a recruiter hounding for nearly two months(calling me multiple times per week) me to go on interviews that didn't appeal to me despite the fact that I made my expectations clear. I finally relented and went on one that seemed the most reasonable of the bunch. Late in the interview, we found a few a changes that the recruiter had made, including lying about my education history. The interviewer must have chewed them out because I didn't hear back from them at any point after that.
Having your own printed copy will convince the employer that it's the recruiter (not you) who is being dishonest.