Only that HR person could really tell you why but I would suggest one of these scenarios as the reason for his/her response:
1) that's just what they were told by someone in legal and he/she didn't know why him/herself
2) he/she wasn't willing to go to the trouble of explaining it
3) he/she is a control freak
4) like his/her kid, you ask "why" too much...just kidding (but half-serious there). :)
Regardless, it's unfortunate you weren't answered because it's an extremely important aspect with legal ramifications. As such, I can't think of one good reason why a good HR person wouldn't feel obligated to tell you, particularly if they have the nerve to ask you do them the favor of taking on the responsibility of interviewing, assuming he/she knew the answer (see #1 above).
In the scenario you've explained, one copy of the resume must be placed in the person's employment file (electronic or hard copy since I'm not sure how the candidate sent it and/or what your company's file-keeping practices are). Other resumes printed for reference (such as your copy) would not constitute an employment record UNTIL you make notes on it. By telling you not to take notes on it the HR person was prohibiting this scenario because all notes are, by law, an employment record.
Federal law mandates retaining employment records for 1 year past the hiring decision (hire, as well as failure to hire, promotion, etc.). An employer must abide by the employer's state regulation, which may be longer than prescribed in the Code of Federal Regulations. Here in Ohio retention for employment records is 6 years, which is vastly different than the CFR so it's imperative to know the state regulation. If you are only interviewing under the direction of others, you might want to familiarize yourself with the regulations but the leader of those interviewing should provide training, including such guidelines as notetaking. However, if you're in a position to be conducting interviews I would be lead to believe you produce records other than employment records which are likely controlled under the federal and state record retention requirements and you should certainly know those to avoid issue.
As for the comments regarding electronic vs. paper resumes, you wouldn't exactly takes notes on electronic copy would you? The only risk would be associated with hard copies so they should be controlled and perhaps that's what your HR person was attempting to do (rather poorly I must say). A good HR person would ensure any packets or copies they distributed were accounted for after the conclusion of the interview.
As for those commenting on destroying notes, same as breaking any law it doesn't matter until you get caught. I would suggest in the future refraining from making comments which could implicate you and your company in a court of law. I see a lot of speculation and passing along of word-of-mouth (possibly disseminating misinformation). Should someone contest a hiring decision and it be discovered you were, in fact, taking notes during the interview and could not produce them I don't think that would go well for your case. Especially if you yourself were found to making comments on a social media forum admitting having destroyed notes in your past.
FYI - My company uses lists of standardized questions (based on position) and a separate packet on which notes are to be made. The form has a field for recording an objective score for each "competency" (category), which should be supported by any notes. Best practice is to utilize the same question (or set of questions) from each competency for every interview to fill the same opening so each candidate is assessed on a level playing field.
Quick reference: https://www.shrm.org/LegalIssues/FederalResources/FederalStatutesRegulationsandGuidanc/Documents/Federal%20Record%20Retention%20Chart.pdf