Using a different word will not change people's attitudes to pets. There will always be those who consider pets to be chattel and those who consider pets to be part of the family.
There is nothing balanced about a relationship with a pet. The "owner" or "guardian" must supply 100% of the pet's needs. Those needs extend beyond just food and water. Socialization, friendship, discipline, love, and health care are all necessary.
I cohabit with a Quaker Parakeet named Brimley and I am definitely not his "owner". Hubby and I have modified many aspects of our lives to accommodate him. he truly rules the roost.