Fortunately it's not true. Sysco has 17% of the market according to Morningstar:

https://www.morningstar.com/company-reports/1327868-sysco-re...

Sysco isn't the only one, but it is one of the few.

If you start looking at the distribution centers of these companies and the competitors, you get a pretty clear picture of how concentrated things are.

The drop off for the distribution centers of the top 3 is stark. [1]

[1] https://abasto.com/en/advice/food-distributors/