Having thought about this some more, I might be inclined to be a little more lenient on judging what is solidly embedded. I don't think "play it as it lies" envisioned a Toro aerator. Having said that, you still need to follow the definition of a Loose Impediment the best you can.
You said match play, which is a little different anyway. If you and your opponent agree on a loose impediment, again believing you are applying the rule correctly, you don't need me or anyone else to rule on it for you. If you and your opponent agree it's done.
Thanks...my one potential opponent is a guy I have played with a good bit and doubt there would be any issues. I don't know the other guy, but they are trying to pick up after the aeration, so I think the incident the other day was in part bad timing.