I consider such reports "highly credible". I would not take any definitive action based on them alone. I simply do not have your sources. Don't want to know them either.
I am sympathetic to your request ("Do NOT doubt me"). I have seen reports from health care workers who would be identified and fired in an instant if those details were made public. I would not expose them to that risk. Some discretion is necessary.
We still need a specific pilot name, a flight number, and a date. An anonymous source will do just fine. Somebody knows that person. There would be too many possible sources to track down a leak.
No amount of corporate spin can undo the damage if such information gets out.
Even an obituary would be nice. Of course, it’s not going to say ‘Delta pilot died during flight after receiving vax’, but are there any obits of a current Delta pilot who died recently? Most obits mention where a person worked and what they did. Not all, but most.