Ketubot 24: Could Kohanim Collude?

What happens when 2 people claim that each other is a kohen? Is that sufficient, or is a third person needed to corroborate, such that each person has 2 witnesses confirming his status as a kohen? The answer is found in donkey drivers or merchants, who are presumed to be more likely to collude, among other examples of trustworthy business practices (or not). Also, other practices by kohanim that seem to attest to their legitimate status as kohanim... but are they enough??