Sentence: "I can't help you, my company installs and repairs garage doors, but they don't install or repair house doors". When I hear this, I get multiple items of information. The big one is what kind of business the company does and doesn't conduct. The minor item, which could be misunderstood, is that either the company employs me, or I own the company.
The only case where it would make a difference is if the person who asked me about a repair of her front door is a single lady keen to find a rich husband, and would be interested in me if I was the company owner, but not if I'm just a repair man. 99% of the time, the information that could be misunderstood is irrelevant.
And in cases where I mean ownership, it also can rarely be misunderstood. For example: "How much did you earn this year? " "I made $50,000 as an employee, but my company also made $50,000, so the total is $100,000". I own the company, no misunderstanding possible.
So the answer: One, "my" doesn't automatically imply ownership and therefore may be used when I'm not the owner. Two, "my company" could be misunderstood, but that would be very rare in practice. Three, "my company" could be used intentionally to create doubt and confusion whether I'm the owner or an employee. In this case, if my intent is to create confusion, and the words that I chose do that, then surely the words are correct.