If you have signed up for a discount program, that could be the same as signing up as a distributor/rep, in which case you are technically "opening a business" and must provide your SS#. You say you want to be "a wholesale customer" - that's a distributor! That is someone who is buying it wholesale in order to sell retail to others. So the company is absolutely right to ask that info from you!
The company would need that SSN to send you a 1099 form for tax purposes and report it to the IRS, like any other employer. That's the right thing to do. However, you do not have to do that to pay full retail - as you yourself admit; it's about price to you. But honestly, why would a company give you a discount if you weren't planning to resell product? I pay retail at the grocery store, but they bought the stuff wholesale. Any store or business works that way.
My concern is that your friend did not tell you this up front - unless you missed this detail, which is easy to do when you are concentrating on which products you want to buy. Sounds like she may not be particularly well-trained by her sponsor. And you should not be signing up without her helping you, frankly - that should be a service she provides.
There is absolutely nothing wrong with MLM companies in general - in fact, they pay more money to their reps than corporate America does, if they are run right. There are only about 200 companies in the Direct Selling Association, which is an invitation-only, scrutinize-the-books watchdog group for direct sales. Go to the website and click "membership" to find out if they are a part of it. If they are not, find out whether they are just a brand new company and haven't had the opportunity to be evaluated/accepted (less than a year old, maybe a little more) or whether they've never been or don't want to be a member (or worse, whether they've been kicked out).
In any case, it sounds like this is being done properly - if you can be a "wholesale customer" without a monthly minimum, and if you are able to purchase anything you want (rather than a pre-set starter package), those are good signs. Make sure there is a minimum 30 day guarantee on the products if you are a customer, and a business guarantee as a "wholesale customer" (read: "distributor) such as a 1-year 90% buyback of anything you buy but don't open. That's the sign of a great company. Make sure there is free training on a regular basis for those who want to become distributors as well.
If you just want a discount, then you should be willing to give your SSN because the company is doing things right. Let me know if you have any questions about this sort of thing.