In 1974, also, Pierre Deligne had a Fields Medal "withheld", after his proof of the Weil conjectures. That was hypothesised to be prejudice against non-peer reviewed aspects of the proof. I wouldn't read too much into this report about Arnold. I happen to have had a brief conversation with the late Frank Adams about the Deligne case (he was on the committee), and what I picked up there was a merest hint about divisions on the committee that year, when only two medals were given. It seems quite possible that there were several divisive issues that time, and some compromise was made. But I don't think we shall know more than rumours until someone on the committee tells all.
Edit: Now that the source has been posted, I'm not quite sure what to think. The medals went to Bombieri and Mumford. Deligne would have been a third geometer (though Bombieri is also known for analytic number theory). It is plausible that Arnold, at 37, would have been a strong candidate.