Why would a transaction from Armory, sent to the node through RPC for relay to the network and of no relationship to the node's wallet, be stored in the node's wallet.dat and require
zapwallettxes to remove it?

Since the tx went through the RPC, Core can correctly assume this tx is yours. I don't know why it would keep track of it, and somehow I doubt zapwallettxes has an actual effect in this case. I'm going to guess Achow only suggested to use this CLI arg as part of a the standard procedure to clean up stuck transactions
in Core's Wallet. Armory isn't related to Core's wallet, it only makes use of the networking and consensus parts.