E.g.:
I claim that I authored the string "foo bar" with hash "1f2ec52b7743687..".
Now you find a collision and go to court arguing:
>> Your honor, but "3HSSHog*8FF9 z!!!!ady94765&$^#" also has the same hash!
I think the court will still assume that "foo bar" is the correct original, not the garbled collision data you produce. And you still can't deny that the original produces the correct hash.