I have also been in a similar networking group, and, from the sounds of it, probably a branch of that same one the OP is in. They have chapters everywhere.
The purpose of these meetings, if it's the one I'm thinking of, is to seek out referrals for each other, not to pressure everyone in your group to buy/participate. The purpose of the one-on-one meetings is to find out more about each others' businesses so you can find out what kind of clients they are looking for. You're not obligated to refer people to them if you don't personally feel you'd recommend them, but it's a way to form interpersonal relationships on a professional level, to increase the number of contacts who might send business your way.
The purpose of these meetings is NOT, "Here, use my service/buy my products because you won't believe this amazing array of miracle vitamins." Acceptable (IMO): "I sell miracle vitamins from my home-based business. My best clients include senior citizens who are looking for ways to improve their health without drugs; I'm looking for new clients who may be busy young professionals who don't have time to shop from stores." (Or other...we were told to focus each week on a specific type of client).
NOT acceptable: "This is my amazing miracle vitamin; you should buy these, and sign up to be a distributor!! You can make so much money selling these vitamins!! Here's some magic water too, that cures everything from a hangnail to cancer. You should come to a presentation this weekend!!"
I quit networking meetings altogether, in part because I was tired of the MLM pitches aimed at me. (And not just MLM pitches, but every desperate person in an oversaturated industry wanting to redesign my website, plan my finances, etc etc. I realize I was also there to pitch my services, but my approach was that I wanted referrals, not to solicit other members to buy).
I had the same dilemma as the OP, and in retrospect, I think it would have been best to say, "I'm not interested in buying for myself, but please tell me about the clients you are looking for."