I agree with your concerns. But my comment was talking about "typical server logs" and HTTPS-POST vs HTTP-GET, while yours is addressing different issues.
I addressed why what gets in logs doesn't matter: if their server is compromised you have to assume you are boned anyways. And I don't understand why is your comment would be talking about "HTTP-GET"? The API in question is dealing with HTTPS for both GET and POST requests.
I don't understand why your comments pointing out details of the http spec and common-sense security considerations are being downvoted. I guess they are coming across as overly 'stident'? Anyway, I've found them helpful. Thanks.