The problem with ash is due to how jet engines work: they push air through them, which is heated up significantly. The ash melts and becomes glass which can damage the engine.

The machine they flew in is a Piper PA-28-181 (Archer II), which looks like this: http://iowaflighttraining.com/wp-content/uploads/2015/11/Arc...

Ash still isn't a great medium to fly in, but at least they won't fly through (a high density of) glass particles.