I think we need some facts:
casperOne did not delete the answer, another moderator did. The answer was deleted because it contained only a link. Link only answers are extremely problematic for us due to link rot. The action that the other moderator took was appropriate
There is no conspiracy to remove competing answers. If we were all twelve years old, I might consider discussing such a notion. Since we have to be at least 13 to use Stack Overflow, I'm not going there. If the answer did not warrant action, the other moderator (who is the most senior on our team) would not have lifted a finger. casperOne did just what you would do, he flagged the answer for a moderator to review, and he wasn't alone in flagging.
It is extremely common for us to find problematic posts that could also create a conflict of interest if we, as a participant, could benefit if we took action. While there is no official rule regarding what to do when that happens, every one of us asks someone else to evaluate and handle it. Notice, I said evaluate. Not once in my tenure have I, or any other mod I know been asked to do something inappropriate by another moderator.
The action that was taken was purely due to the fact that your answer did not meet our quality standards. Nothing less, nothing more. casperOne did not, in fact, use any of his moderator abilities on that question. He used the same privileges available to any other user with sufficient reputation to flag a post.
Edit
Per your comment, this has everything to do with the specific question since the scenario didn't happen. However, as I commented under Brad's answer:
Worth noting that the reason no official rule exists is because it's never been a problem. We've all just naturally not taken action that could benefit us unfairly, and asked someone else to look into it. Now that it's actually been questioned, perhaps it should become policy.
I'd support that. A conflict of interest could arise if we:
Modify the CW status on a post that we own
Delete upvoted posts that we own which non-moderators could not do with a single vote
Delete any answer to a question that we've answered which is not obviously a:
SPAM drop (gucci bags, etc)
"Me too! Me too! Did you find the answer to this?"
"asgjsdhgjshhkds U ALL SNIFF LLAMA FEET FTW!!"
Delete comments written by others under individual posts we own, barring the same criteria
In the above cases, it's better if we just flag and let another moderator handle it. I also propose no changes to the system, only that we directly address the above in our code of conduct, which (beyond thisthis) has not been canonized.
This has never been, and still is not a problem in need of a solution in the form of policy or anything else. Yet .. it probably wouldn't hurt anything to plainly state what we all took as obvious. I don't want to look back later and wish we had.