Is it true that removing thin capsules could cause damage?

There's definitely some truth in what your plastic surgeon has told you.  Removal of any type of capsule, thin or thickened, can potentially  lead to "damage" of surrounding tissues.

Generally speaking (in my opinion), unless the breast implant capsules have thickened (and/or are otherwise symptomatic), are associated with the ruptured silicone gel breast implants, or if the patient has concerns about "medical conditions" related to the breast implants, capsulectomy is not universally necessary. For these patients, en bloc removal of breast implants is a good procedure.

***On the contrary, capsulectomy can expose patients to additional risks, such as bleeding, size loss, contour irregularities and other serious complications. In other words, any maneuver performed during surgery exposes patients to additional risk (morbidity). For example, attempting to remove very thin capsule densely adherent to the patient's rib cage may expose the patient to significant bleeding and/or entrance into the thoracic cavity.

  The good news:  breast implant removal surgery is a very well-tolerated procedure with minimal discomfort,  compared to first-time breast augmentation surgery. Patience is definitely indicated after removal of breast implants; it will take many months for the skin to “bounce back” and for you to see the final appearance of the breasts.

I hope this helps. Best wishes for uneventful surgery and an outcome that you will be very pleased with.

Concur with your PS's advice. If areas of the capsule are difficult or dangerous to remove, the risks of removing thin, pliable capsules outweigh leaving the capsule.  If there are calcific components, or silicone granulomatous material, or if the capsule is deforming the breast tissue, then removal of the capsule may be warranted.Kenneth Hughes, MD, ABPS Board Certified Plastic Surgeon
Los Angeles, CA

There is a risk of damaging surrounding tissues when the capsules are removed, but it can be done if desired.  Typically if the capsules are thickened or the implant is ruptured, then removing the capsules is recommended.  If they are thin it is an option to leave them behind when the implants are removed.