There is one error in your logic.
If they have an interest in buying the company, they don't just need your shares, they need my shares and they need Respert's shares and all of the other other shareholders. Even to obtain merely a controlling interest in the company, they need much more than that.
The current market price is based upon supply and demand for the currently available shares. Most shares are not on the market at any given time.
Make a run for the purchase of a controlling interest in the company, and the share price will shoot way up.
Then, when they hit 5%, they must disclose their holdings. And, then again at 10%, I believe. What do you think would happen if Merck (or any other BP) was listed in an SEC filing as holding 5% or more of our stock?
That's likely why they don't telegraph their interest by buying up cheap shares like that, as at some point, they will need to make a tender offer in order to obtain sufficient number of shares to take over the company.