The keyword is "opportunity cost". By walking two Eevee, you are losing out on four candy for a more valuable species. Is that sacrifice (considering the risk that the rumours may be unfounded) acceptable to you?
What are the potential gains? I doubt that Umbreon, even with an incredible move, could threaten Tyranitar. Do you have enough Psychic-type attackers? Imagine what Espeon (already tied with Alakazam as the best non-legendary Psychic-type for all generations) could be with a special move.