On the other hand tree rings can be selected from trees in really remote areas where this unnatural excess heat isn't present. Same conditions for centuries if you go into deep old growth forest like Siberian forrests. But as noted previously, the growth rates of trees isn't solely due to temperature. So there is some inherent ambiguity in the results. And if you find one oddball tree that doesn't match any others and let that totally skew all the data by intentionally keeping sample size really small so the outlier tree dominates, well, you can create a scary looking hockey stick graph from it and it sounds really scientific ("based on 1,000 years of tree ring data from old growth forest ..." ooh, sounds really complex!)
I have no problem with using tree rings as a proxy for temperature trends. My objection to using them as definitive evidence of exact temperatures stems from what you pointed out, that other factors besides temperature affect tree growth. There is absolutely no way to derive a temperature to within 1/100 of a degree by using tree rings.
If you want a historical record, you need to either use the same measurement modality across the time period under study, or you need to validate that a new modality is functionally equivalent to an old one. I doubt that it is possible to validate the use of tree rings vs. thermometers as being equivalent modalities.
I think that the most accurate methods of taking measurements involve satellites, since they can look at an area and come up with a temperature based on the average pixel temperature. That method smooths out the hot spots that are problematic for trying to place ground thermometers.
If all a scientist is doing is trying to get an idea of the climate over the last 1,000 years, then tree rings are perfectly adequate for the job. But trying to fear-monger about how the earth is 1 degree hotter than 1,000 years ago, ergo anthropogenic global warming, is not supported by the evidence.