The information we see is:
- Your username,
- The close reason or your message, if you flagged for moderation attention,
- How long ago you flagged,
- If you also voted to close (for question flags, and only for users with 3K+ rep), and
- If you posted one or more comments (just a count).
Everything else, including edits, we see exactly like you do, by visiting the post. We don't have to actually visit the post to action the flag, but AFAIK all of us do, we don't get that many flags per day (about 50 or so).
I don't know why you couldn't re-flag, I'm 99% certain that you can flag for moderation attention even if you flagged the post previously. You can't flag a question as off topic twice, that wouldn't make much sense, but you can use the custom flag as many times as you want.
You shouldn't worry (much) about re-flagging to contradict an earlier flag, although if you do you should expect at least one of your flags to be declined. However, please don't make a habit of flagging when you can edit first. It's perfectly understandable if it happens once or twice, some times the edit is not immediately evident, but if it happens all the time, you'll get on someone's nerves (and if you are really unlucky, that'd be me ;)
As for the question in question, the moderator who handled your flag did notice your edit, and even acknowledged it in a comment, all is good ;) That said, if you happen to regret another flag in the future, flag for moderation attention, and thoroughly explain in your message why you're flagging, mentioning edits and everything else that's relevant. It'd be quite puzzling to see two flags on the same post from the same user, and you'll help us understand what's going on with a clear and to the point message.