Yeah, I agree with @apg – you seem to just be restating what the author is saying (I don’t think he’s confused at all). Also, I don’t think your last sentence is correct:

Thus there are no locally declared arrays.

You can definitely have a locally-declared array. From the POSIX spec:

If fewer arguments are supplied in a function call than are in the function definition, the extra parameters that are used in the function body as scalars shall evaluate to the uninitialized value until they are otherwise initialized, and the extra parameters that are used in the function body as arrays shall be treated as uninitialized arrays where each element evaluates to the uninitialized value until otherwise initialized.

So if you use a parameter inside a function as an array, but the caller doesn’t pass that array, AWK creates a fresh new local array each call (which works recursively too). It’s still stack-based, so still doesn’t need a GC. Consider this recursive function:

$ cat t.awk
BEGIN { f(2) }

function f(n, a) {
    a[n] = 1
    for (k in a) print k, a[k]
    print "---"
    if (n) f(n-1)
}
$ awk -f t.awk
2 1
---
1 1
---
0 1
---

Note how each time it’s called, the a array only has one element. A fresh one is created each time == local arrays.

Compare that to this one, where we pass in a single global array from above, and note how the array gets larger as we add to it:

$ cat t2.awk 
BEGIN { f(2, a) }

function f(n, a) {
    a[n] = 1
    for (k in a) print k, a[k]
    print "---"
    if (n) f(n-1, a)
}
$ awk -f t2.awk 
2 1
---
1 1
2 1
---
0 1
1 1
2 1
---

Only function parameters are local to the function

I’m now confused. How is what you are saying different from what the author says?