Well, to address your points:
Yes, you can write functional code in (most) imperative languages... at least those that support recursive function calls. Although really the way to make a functional-like factorial call in perl would be like:
sub factorial { $_[0] == 1 ? 1 : $_[0] * factorial($_[0] - 1) }
That is: each function is only a single expression. Haskel goes a little further, though, because it supports function-dispatch by pattern matching... but this is the general case of how one writes functional code in perl. No assignments, no loops, a single expression. While it's true that any decent functional language interpretter supports automatic optimization of tail-recursion, that is a property of the interpretter, not of the language itself (except to the point that specifically optimized idioms usually become a part of any language, if only in the developers training of best practices).
As far as the functional language interpretter having state: well of course it does. It's ultimately implemented in machine code, and machine code on any computer is imperative. It has state (memory, registers, etc). It is a sequence of commands. So on. The point is that this state is not a mechanism employed by the programmer in his/her functional programs, it is merely an artifact of how the functional language interpretter is implemented on an inherently imperative computation machine.
Update: forgot the "- 1" in the code. Oops. I was just trying to make a point, anyway... it was obvious what I meant.
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