Yeah, someone actually did that, or the subject would never have arisen.
If you wish to delete a post, for whatever reason, before anyone has responded, why would anyone care? For that matter, no one would even know. However, after someone responds, the software will no longer allow you to make a deletion. Not so with edits, so one has to use discretion. Incidentally, making an honest mistake is no reason to feel embarrassed - it's just part of the learning process.