Yes, so you’re technically correct. :) What’s interesting is that there actually is a distinction between the “org” and the “customer” in the SWIP process, but IME the “customer” reallocation is rarely used, and certainly not for cases of a single IP. So yeah, if you’re renting a VPS or a dedicated server with anything less than a /24, you have basically no control over your IP reputation.

That said, providers generally do keep records of which IP is associated with which customer at which time. That information is just not publicly available in real time.