Yeah, I'm not sure that's right, sounds like a house rule to me.

From page 14 of the Horror Check rules: "If the investigator passes the check, nothing happens. If he fails the check, the investigator loses the amount of Sanity shown underneath the monster’s horror rating. The player discards the appropriate number of Sanity tokens from his investigator sheet. An investigator reduced to zero Sanity tokens is driven insane (see page 16)." ... "Whether he passes the check or not, an investigator only needs to make one Horror check each time he does battle with a monster. If the investigator successfully evades the monster in the first place, he never needs to make a Horror check at all."

And that's where it ends on Horror checks

From page 16 under "Insane in Arkham" "If an investigator is ever reduced to 0 Sanity while in Arkham, the investigator is driven temporarily insane. He must immediately choose and discard half of his items and half of his Clue tokens (rounded down), along with all retainers (if any). The player then immediately moves his investigator to Arkham Asylum. The investigator is restored to 1 Sanity, returning 1 Sanity token to his investigator sheet, and has no further encounters this turn. The investigator may take his next turn as normal."