The acid is the product

What the definition is actually saying

Read it as a description of a transformation rather than a category. You start with something that would not keep, you add acid, and the finished product sits below a threshold where the organisms that matter cannot establish. The regulation is not describing a flavor, it is describing a barrier, and the number is where that barrier is considered to hold.

Why the cucumber matters to the definition

The cucumber is the low-acid food in that sentence. Left alone it is not shelf stable and nothing about washing, packing or sealing it changes that. Every instruction on this property that looks fussy about vinegar strength or about proportions is protecting the one thing doing the preserving.

Why jam is not in this regime

The exclusion list in the same section names jams, jellies and preserves. They are excluded because the fruit was already acidic and the sugar does additional work, so the product was never a low-acid food with acid added. That is why a jam maker can sell from a home kitchen in states where a pickle maker cannot, in the same preserving category, under the same roof.

What follows from being inside it

Being an acidified food is not a label, it is a set of obligations: a process that has been established and filed, records that show it was followed, and a pH that was measured rather than assumed. The rest of the selling section on this property is the consequence of this one page.

Which is the useful way to hold it: this is not a rule you comply with alongside making the product. It is a description of what the product is, and everything else follows from reading it that way.

References