There is a great deal of misinformation, misunderstanding, and fear mongering with the use of the term "transmission flush." It is used for many different service types.
The current methods I am aware of allow the transmission's internal pump to cycle old fluid out, while a "machine" cycles new fluid in. This "flush" method is 100% safe, and is a far better approach than a drain and refill (which only replaces less than 50% of the fluid each time it is performed), as it replaces almost 100% of the fluid in one run.
The reason the transmission flush has a poor reputation is due to the use of dex3 fluids, which were far lower quality than the dex6 fluids we have today, being serviced in transmissions that were WELL past their required service life. Those owners typically brought in transmissions that were having shifting issues, expecting the fluid to resolve those issues. The damage had already been done by that point, and the transmission flush did not prevent the impending total failure from occurring. Another reason is due to pressure-fed flush machines that did not utilize the internal pump to cycle fluid through, which could dislodge oxidation deposits left behind by the aforementioned poor quality dex3 fluids, which would then clog up very small valve body passages. This again is the failure of the customer in maintaining their transmission at proper intervals, not the flush method itself, as those deposits do not form when the correct service intervals and driving conditions are followed. In those times, owners who expected to tow regularly were also advised to install auxiliary transmission oil coolers to keep the dex3 spec fluids from breaking down under heat.
I have a tutorial written for performing this "flush" in your own garage, provided you have a method to scan for transmission temp. I've had several mildly technical owners perform this process safely and very effectively, with excellent results, using AMSOIL Signature Series ATF.
Since most of these pressure-fed machines have been decommissioned due to their reputation and replaced by machines that simply replace fluid expelled by the transmission's internal pump, they are no less "safe" than a standard drain and refill, but they do waste less fluid while replacing a far greater percentage of the old fluid. If you fail to service your transmission at the required intervals, neither method is guaranteed not to reveal more problems that would have already been caused.
With respect to these specific transmissions, GM used corrosion inhibitors to prevent internals from rusting during storage at dealer lots, which turned the oil black and also compromised shift quality. I was told that they stopped using these corrosion inhibitors at some point, but the color of the fluid is a consequence of these corrosion inhibitors, not the break-down or oxidation of the fluid itself. Color is NOT an accurate or reliable metric of the condition of a lubricant.