Maybe, maybe not. I skimmed the article because I don't have the stomach to read the whole thing, but it seems to be a feeler. Their it out there and check for the response. "20 companies, but we can't say who". That's convenient. It just says Google and Facebook, which are in California. No surprises there.
FedEx being a nationwide company with employees that have many different viewpoints will have a very hard time with something like this. Morale already being on the low side, people don't care as much. I know road drivers that miss their gates intentionally to annoy dispatch as a form of retaliation. This will make stuff like this worse.
Also, FedEx and other employers aren't liability exempt like vaccination creators. AFAIK, the vaccinated are more likely to spread ThaRona and are capable of being infected. The vaccine is just supposed to make it not as bad, but there are adverse reactions for some people. FedEx doesn't want those problems.
I saw OD is offering 500 dollars to employees for getting vaccinated. I haven't heard anything like that from FedEx which sounds like they're trying to stay out of the discussion and leaving it up to you. That's how it should be. It's also not hard to fabricate one of those cards. Create a market for it and the black market will be all over it.
The question is, is FedEx prepared to deal with the blowback of something like this?