You're right, except the solenoid in the Type-R is more like a sear-tripper solenoid than the little micro solenoid valves found in a T1 and other "high-end" markers. Here's a pic
of the Type-R solenoid valve disassembled.
Instead of taking advantage of a delicate balanced valve, the Type-R and Wrath solenoids use a "brute force" method: lots of electrical current creating a powerful magnetic field to move a plunger in a valve that isn't much different than a 'cocker 3-way. The brute force method is noisier, but far less expensive.
So as far as the board is concerned, the "solenoid" is the same as a sear-tripper - and requires the same large dump of current. Hence the big capacitor.
Edit: As usual, someone else is smarter than me and better with the pictures and explanations. Check out ydna's site
The Type-R and Wrath have direct-acting solenoid valves, while T1s, Intimidators, and their ilk have pilot-actuated solenoid valves.
The FASOR aspect isn't as important, especially with aftermarket boards that can precisely control dwell.