Lol a donation cannot be written off by two entities. Americans would need to itemize their deductions, which very few do.
The company does not write off the donation. It’s not their donation, it’s your donation. The company is a collector only.
Sure, the more correct wording would be “neither the customer nor the company are taxed on the donation”. Assuming the customer itemizes their taxes, which a you’ve pointed out is rare.
I’m trying to speak at the level of people who post stuff like the OP. Some of the details don’t shake out correctly but I’m not trying to get in the weeds of US tax code here if the main point holds up.