What should have happened when the FAs discovered the food was still cold (no doubt after several complaints by passengers), is that all the food that had already been served should have been taken back and binned. There is no way to say that 'it's safe to eat'.
But what also should have happened is that every passenger who was served cold food should have refused to eat it and asked to have it taken away and binned. You didn't do that and that means you share responsibility for the outcome (assuming it was indeed the food that was responsible for your illness). If you are responsible for the outcome, you cannot then try to put all the responsibility back onto the airline.
What did happen no doubt is that someone in the flight crew said, 'if we take them all back, we will have nothing else to serve them. There will be a riot, tell them they are OK to eat.' Someone did what some people always do, that is, what is easiest for them.
Regarding it being fully coooked and safe to eat, that's a common misconception. It all depends on what happens during the cooling and re-heating periods. People often take say a leftover cold chicken leg out of the fridge and just eat it without any ill effects. But it is not guaranteed by any means. Here is a good description of the issue.
https://www.theskepticsguide.org/ask...reheating-meat
My wife has a medical background and NEVER serves any meat, fish or poultry without using a thermometer to make sure it has reached a high enough temperature. She would never have taken a second bite of what you were served or allowed me to do so. If I look at a cold chicken leg in the fridge, she just gives me 'that look' and I know I have to heat it first.
So bottom line for me on this one is that they should have taken it all back and weathered the resulting 'storm' of protest when there was nothing else left to serve you. Equally, you should have refused to eat it and insisted it be binned. The airline should then have apologized to all passengers for a mistake that happened for whatever reason and the passengers should have 'gracefully' accepted that apology and nibbled on the cookies they handed out instead or whatever.
But that would be in a perfect world.