Correct. Arrow (who also designed Matterhorn's tubular steel design) designed IasW's flume ride system. Then they modified it for PotC.
By the way, for coaster purists... Matterhorn is often incorrectly listed as being the first steel coaster. Not so. It was, however, the first TUBULAR steel coaster.. Other "flat" steel coasters came decades upon decades before.
As for Matterhorn's other "first," was it the first "indoor" coaster (at least partially)?
Or was it a "first" because of Arrow's brake/boost system (now evolved into trim brakes)?
Or a first because of using water to slow it down? (EDIT: obviosuly know the answer now. Silly duplicate posting with the OP)
Is that enough guesses?