This is a situation that would make me very uncomfortable for three reasons:
1) How do you know that you are in fact getting what you are being told you are getting if you do not have the right to examine the books and records of the business. There is a funny movie, "The Producers" where the promoters sell lots of people shares totaling far more than 100%. If you are being told you will be getting 10% of the company how do you know that there are not 500 other people also being told they are each getting 10% as well?
2) In a small business it is generally a good idea to know who your "partners" (used loosely, I know this is not a partnership) are. If one of the people is engaged in illegal or terrorist activities do you want to be part of the business? If you do not have the right to know who the shareholders are do you really think that is to your benefit.
3) Openness and transparency are important to protect investors. That is why larger firms have outside auditors and file annual reports that anyone can see. If you are not allowed to see the books and records of the company (which would list who owns what stock), how are you to know it is being run properly?