Adult "son" & family living with me

My significant other & I have been living together for many years.  His son lived with us growing up & I consider him my son, but "technically" he is not.  He and his family of 5 moved back in with us this year.  We are covering all the expenses, except for food for them.  To feed their family, they are getting state aid.  We recently asked that they start contributing a small amount to help with the living expenses.  They said if they do that they want to claim it as "rent" with the state. 

Since I am the sole owner of the home & not "technically" his mother, would that count as income for me? 

Thank-you.