The idea that Donald Trump would be the person making an offer to the CEO of a tiny startup for a non-existent, as yet, vaccine should trigger alarm bells, as that's not how these negotiations work, at all.
If you want to understand how these things actually work, read this article:
https://www.fiercebiotech.com/medtech/fda-grants-roche-coron...
Additionally, US government officials are on the record stating that any discoveries would be shared with the world. Plenty of governments are providing funding to labs all over the world, this is not unusual behavior.
> The U.S. government has spoken with many (more than 25) companies that claim they can help with a vaccine. Most of these companies already received seed funding from U.S. investors... any solution found would be shared with the world
https://www.reuters.com/article/us-health-coronavirus-german...