Seems to work, with rough edges.

readline_autocomplete_file_names.py

import os
import readline

AUTOCOMPLETE_CACHE = {}


def completer(text, state):
    global AUTOCOMPLETE_CACHE
    buffer = os.path.expanduser(readline.get_line_buffer())
    cached_response = AUTOCOMPLETE_CACHE.get(buffer, [])
    dir_name = os.path.dirname(buffer)
    if not cached_response:
        complete = os.path.basename(buffer)
        cached_response = [p for p in os.listdir(dir_name) if
                           p.startswith(complete)]
        AUTOCOMPLETE_CACHE[buffer] = cached_response
    try:
        return cached_response[state]
    except IndexError:
        return None


readline.add_history('~/.ssh/')
readline.set_completer(completer)
readline.parse_and_bind('tab: menu-complete')

pick_file = input('file: ')