There’s never anything wrong with getting a second (and sometimes even a third) opinion when you are in doubt. It may be helpful for you to know that studies show that people can have severe symptoms with a minor tear of the rotator cuff. And it’s possible to have no symptoms despite a massive (full-thickness) tear.
There is also plenty of evidence that a conservative (nonoperative) approach can be very successful. With strengthening and flexibility exercises, it is possible to rehab the rotator cuff and prevent the tear from getting worse. If the tear progresses to involve a full-thickness (Stage II) tear or to involve other tendons (Stages III and IV), then surgery is more critical.
When the biomechanics of the shoulder are altered by a rotator cuff tear, rehab can become more challenging. Prevention of tear progression can also become a difficult target to reach. But you can be successful with compliance to the program and avoiding overloading the soft tissues until healing has occurred.
A recent cadaver study looking at critical tear size when surgery should be recommended highlighted these conclusions. Stage I is the place to get started with rehab. Stage II requires careful monitoring during rehab with progression to surgery if rehab is unsuccessful and/or the tear gets worse (becomes a Stage III or IV tear).
With your diagnosis of a Stage I tear, you are considered a good candidate for rehab.