Can a research group be formed without a PhD in charge?
A PhD is a degree supposed to develop (and later demonstrate) the skill of being capable and ready to do independent research. The degree to which that is achieved can vary massively, depending on institution and supervisor. 

It is quite possible (and not at all improbable) that a non-PhD person can outshine the PhD person, but, per default, the latter enjoys a priori the expectation that they know more about the process of doing research than the former. However, this is no reason at all not to form a group of interested people, with or without PhD. A PhD member is not a guarantee of success and the lack of one does not presage doom.

The case you mention seems to be of someone who does not want to see a competing group being created (depending on the convention of your location). That being said, make sure you have knowledgeable people in the group. The reason why many countries have a research group led by a professor (not just a PhD) is that the latter not only know how to do research but have had a broad exposure to many methods and perspectives.

Good luck!