Warning: I may be totally projecting.
I'm getting a possibly inaccurate vibe that the secretary may have thought that perhaps the level to which you were disclosing on the phone was just the tip of the iceberg to which you disclose to friends at home/the bar/at parties/on the rapid transit, whatever.
She may have been thinking, "If this is what she discloses on the phone, blatantly in front of me, what might she be disclosing to people in the aforementioned situations?"
In a perfect world, she was just trying to make sure you weren't disclosing unethical things to other people in private, when she heard you disclose a very borderline-private thing over the phone. Or, maybe she was just feeling superior and snarky.
If she truly thought you were being inappropriate, the right thing to do would be to mention it to your supervisor. However, maybe at the risk of going over the top, she may have just thought she'd plant a seed without "ratting you out."
Giving you "homework" was WAY over the snarky line, however. Way over. Dang. Having worked in admin support for dozens of different kinds of businesses, I have learned a lot about how lots of types of businesses work, but she was in no position to try to pull rank on you or tell you what to do.
Giving her the benefit of the doubt, it's also possible that she is extra sensitive about disclosure issues because she or a loved one is in therapy herself/themselves.
This is probably totally unrelated, but I'll share anyway. I've been doing a little receptionist work on the side this year at a very fancy Mercedes-Benz dealership on the weekends. Hardly anyone calls the dealership on a Saturday because service is closed on the weekends (how do you like that!) so I was able to read and do research while getting paid a little bit. However, it was impossible for me to not hear the things that the salespeople said about customers and their fellow salespeople.
It is an interesting position to be in, because everyone assumes I do not have a high school education, and am therefore unable to understand anything. Booya.
Goofball salesperson, "So what are you reading there, War and Peace??"
Me "This is the DSM-IV-TR. I'm actually in graduate school for psychology. It's fascinating. <insert 'can you read my mind' comments here.>
Me "Oh, reading minds are for psychics. But you must use a lot of psychology here at the dealership to sell cars."
Goofball "Oh yeah, people want MB because of the status, not because of reliablility or a good repair record."
Me "Wow, interesting. Does anyone come in wanting a certain, make, model and year of car that Consumer Reports says is the most reliable, and won't settle for a make, model or year that was considered by CR to not be reliable?"
Goofball "Huh? No. People want these cars for status, not for quality. Besides, Consumer Reports is totally biased, so is Kelly Blue Book."
Eek!!
Sometimes people think the receptionist is blind, deaf and mute, when in fact I came to understand a lot about the business of selling cars. I never gave a word of advice, however, because I knew I knew nothing about selling potentially unreliable cars to people who want to look superfly. Yuck.
As I said, this is probably unrelated, but perhaps interesting. There is element of psychology in every business. I can imagine that if a person had worked as a receptionist for the dealership full time and had some kind of agenda, I can imagine they might give some unsolicited advice. WRONG. Read your job description. Do your job to the best of your ability. Learn if you can, but don't assume you know what's going on from hearing one side of a telephone conversation.
Hearing this and that, here and there can make some people think they know everything. Sounds like that was what was going on in your case.
It might make sense to mention it to a superior, up to you and your judgment and if she ever does it again. Especially concerning the word "homework." Condescending.
Anyway, I hope she had the best of intentions and won't be eavesdropping in the future. Yeah, right.
Now you know which phone NOT to make calls from.