I think this theory assumes that he wasn't as good a spinner as the specialist that might come in, and that he was no better a FM than the specialist who might come in. So if the conditions looked favourable to spin, it was better for the team to have the better spinner in the team, and have Sobers in the 'take the shine off the ball' role. If the conditions were looking good for the quicks, they would in theory go with the extra specialist quick, who would be as good as Sobers, and hence Garry probably wouldn't get many overs as a quick, but would get thrown the ball when the captain decided the quicks needed a rest while some spin was bowled.
Again, as I said, I don't know how often this theoretical situation played out, but that is what people are suggesting.
EDIT: There were also obviously matches when he bowled more than one style. If the ball was swinging, I'm sure he'd have a go at FM, regardless of whether he was the theoretical spinner or not.