> GCing has nothing to do with a language being functional
Yep, I didn't say it did! You mentioned Haskell and OCaml as counterexamples. I referred to them as "the compiled functional languages". This isn't a claim that only compiled functional languages do GC.
> Interpreters don't do GC
Sure they do! One example: Ruby (the original interpreter in C). It has a full mark/sweep collector that traverses user data structures. Custom object types implement their own 'mark' routines, so it's fully precise. (I've implemented a C extension that uses this API.)
Another example: often, Java runtimes interpret Java bytecode on the first pass, before JIT'ing, to give fast startup on cold code. The JRE would be written in C or C++ (non-GC'd), and Java is GC'd.
In general an interpreter can add any additional or different semantics it needs to on top of the host language's semantics. I don't think your call-by-value claim is correct either, because function calls in the interpreted program do not map one-to-one to function calls in the interpreter. (The interpreter would generally manage a data structure representing the interpreted program's stack.)
My goodness, this is going off the rails. Sorry to OP for derailing. Just trying to fix things that are Wrong On The Internet...