The description you posted is easily misinterpreted.
As Mr Hunter suggests,there may be two swithes added
to your starter circuit for your 'protection'.
(neutral and clutch-pedal positions)
Yes it can be push started. And as soon as you
get it home I urge you to UN-child-proof what I expect
to be a 1987 200 series. Solenoids are generally easy
to swap (or fix) but I cannot attest to their being
'universal'.
Like Mr Hunter, I think it's a safety-feature gone awry.
Personally, I like the comfort of knowing I can crank
(with starter)
my car onto a trailor when the timing belt goes south.
*it happens!
Good luck!