There are too many loose ends in your question to answer it fully.
What do you mean by, "through my company not a 3 rd party agency"? Let's say you are performing work for company "A." What is "my company"? Is that a privately held company you own and control (truly my company)? Or is it a temporary staffing company that has assigned you to A? What do you mean by a "3 rd party agency" and what differentiates that from "your company"? Who reports and pays your taxes? Who pays the employer's share of Social Security? At the end of the year do you get a W-2 or a 1099? You say you have a 401(k). Who provides it? When you get paid, what employer name is on the paycheck?
The answers to all of these questions will shade the answer you are looking for.
In the simplest terms, unless you can clearly demonstrate that company A is not hiring you for some discriminatory reason, it is free to hire or not hire you for any reason, including the color of your shoes or the flip of a coin.
You say the postings are available to all workers. That doesn't mean the jobs are. It's a subtle distinction, but it's not unreasonable and it's legally defensible.
You should talk to your employer (not company A) and ask for an honest assessment of your chances to be hired as a permanent employee at A.
Part of your question deals with a very complex area of employment law called "co-employment." It means you are effectively "employed" by two "employers": the one who pays you and the one for whom you do work. Your rights as an "employee" of each company, and the obligations of each, make for dizzyingly complex employment law, far beyond the scope of this forum.
Massachusetts health insurance law is unique, if not complex. Here's a link to the Wikipedia article discussing it: Massachusetts health care reform - Wikipedia, the free encyclopedia. It's not a particularly easy read, but you should familiarize yourself with it, especially if you currently do not have medical insurance.