"The letter references no IRS code or anything."

Why would it? It's stating a useful fact: the work is considered to be in a Combat Zone.

That doesn't mean they got combat pay. Even you noted that isn't how this letter reads and you misstated this in your title

"The "employer" who issued the 1099nec stated in a letter that the income is eligible for "Combat Zone Exclusion"."

It means any provision where Combat Zone matters, is applicable, if the taxpayer qualifies. It's right here, follow the link:

https://www.irs.gov/newsroom/new-law-makes-clear-combat-zone-contract-workers-qualify-for-foreign-ea...

"The new law makes it clear that contractors or employees of contractors providing support to U.S. Armed Forces in designated combat zones are eligible to claim the foreign earned income exclusion."

It sure is helpful when you stop using the word "employer" with "1099-NEC" because that leads you and your taxpayer clients down the wrong rabbit hole.