A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
A player, 24 September 2007
Hi there...
can a player using 'The Maw's Grave' pay the honor cost on an action, like: - Arrival of the Obsidian Champion (Open: Lose 3 Honor. Dishonor one of your target Personalities with a Gold Cost of 9 or greater. Permanently set his Force to 10 and his Chi to 2. Permanently give him Shadowlands and the ability, "Fear Battle: Bow each Follower with 4 or less Force in a target unit.") - Fight Another Day (Battle: Lose 2 Honor. Move home, then straighten, all units in your army. If this moved a Nonhuman, draw a card.) - and others...
because this stronghold have this text: "...You do not gain or lose Honor...."
Zen Faulkes (rules official), 24 September 2007
Chris Fuchs (rules official), 24 September 2007
Note that both of the examples provided in the question have honor losses as effects, not as costs. Nothing prevents a Maw's Grave player from playing actions with honor loss effects.