The statement from the previous school is meant to be confirmation of why the SA told them he was transferring-- not why the previous school's HC or AD think he transferred. Key difference.
If the SA or his family indicates to the previous school he's transferring for personal reasons, to be closer to home or because of a health issue-- either his or a family member's, then that's what the previous school's statement should say. The previous school's AD submitting a statement claiming the SA transferred for personal reasons and playing time contradicts the SA and will result in denial-- even though the addition of "playing time" is based on the previous school's opinion, which wasn't requested. Even though the new school put together a waiver package, based on valid grounds, that meets every single requirement on the NCAA checklist.
That's how schools like Michigan torpedo waiver approvals, then claim they didn't block anything. They also delay providing supporting academic documentation, bogging down the process. It has been their default response.