Hi @plato,
FYI. I was just browsing the source code (for something else, and remembered this exchange).
Source code of Ido tells me that SPC is bound to ido-complete-space.
The following should do the trick. I tried the second option; it worked on my machine; no reason why the first one would not work, as it is how Ido itself does it.
(define-key ido-common-completion-map " " 'self-insert-command)
or
(define-key ido-common-completion-map (kbd "SPC") 'self-insert-command)