ETA used to sell their movements to anyone about 10 years or so ago. Then it was likely that an advertised ETA (instead of A2836 or A2824) could possibly be true. Later on some TD’s would provide a genuine ETA, but it was a used one from another watch. These movements were in dire need of a service - they were often just literally dunked in oil or bone dry. Therefore a genuine ETA was not a reliable option. A few years ago ETA stopped supplying any of their parts to anyone who isn’t an authorized service shop or their subsidy.
The situation now is that you might be able to personally get some NOS ETA’s people have lying around, but that would never be a working model for a Chinese manufacturer who needs to provide hundreds if not thousands of genuine ETA’s.
Therefore I personally would always go for A2836/A2824 and later swap for a genuine ETA I have lying around just for such occasions if the need arose.
As others mentioned, and I agree, that claims of “genuine ETA” should be taken with a pinch of salt. This is not a financially best proposoition, anyway.