Unless I'm missing something, in game 115224630 I was incorrectly not able to react with shield to prevent cutthroat discarding:
For example:
k plays a Cutthroat.
h discards a Copper, an Estate, and a Doubloons.
h reacts with a Shield.
(there was no react popup or option to click the card prior to discarding)
It's a bug, correct. The Cutthroat was reckless, and the way the Reckless mechanic is implemented has as a consequence that the first "attack part" always happens and the second can be prevented with the usual cards (Moat, here Shield).
It's a known, not yet fixed bug :(