Yes the company retains the rights. It was done at work. My name , several other scientists, and the CEO and her husband(co founders) are on it too. In the case above, probably all patents that come out of where Faucci is the head of has his name on them. If you "borrowed" something from work and did all the development at home, the company has rights to the patent, You have to have exhaustive paperwork that you didn't get anything from them..