They paid more.
https://www.timesofisrael.com/israel-will-reportedly-pay-mor...
So Israel probably didn't really compete with the US for it.
[1] https://en.wikipedia.org/wiki/Operation_Warp_Speed [2] https://nypost.com/2020/12/16/biden-should-credit-trump-on-c...
Edit: Clarity
Not sure why you think this flimsy evidence holds when the author's actual intent is "nationalism is good actually." Vaccine distribution/contracting is significantly more complicated that this binary analysis.
In the medium term, vaccinating US people first and fast is a great way to sell them on building lots of production capacity.