ZAB Controller voiced concern regarding confusion with the 'descend via' clearance on RNAV procedures reference speed assignments.

Narrative

I was working 42 and 49 combined. I had three arrivals; two on the North side of R2306/8 going to PHX; one on the South. The first ASH was filed on the ARLIN3 (non RNAV); number two filed over MOHAK on the South side; then Aircraft X on the North side over SCOLE; number three; filed on the GEELA4 arrival. The ASH didn't have a speed assigned (at SCOLE; the ARLIN3 has no speed). The guy on the South side would comply with 280 knots at MOHAK; hopefully. At SCOLE on the GEELA4; the speed is 280 knots. When Aircraft X came over; they were doing about 70 knots faster than everyone else; the wind wasn't a factor. I asked them their airspeed; they said they were doing 320. I slowed them to 270 indicated. The pilot asked me a question about whether they were cleared to descend via; I asked them to say again and they said disregard. I believe the pilot was implying that they didn't have to comply with the speeds if they weren't descending via. This has been a faulty understanding previously by pilots. I believe the understanding of the pilots; when it comes to speed control; is a significant problem. When using RNAV procedures with no other instructions; the phraseology; and hopefully pilot understanding; is simple. When vectors and; especially; speed control come into play; pilot comprehension is significantly impacted. The RNAV OTG work group has paid significant dividends in fixing problems and enhancing understanding of pilot and ATC problems. I believe the same emphasis should be placed on RNAV arrivals; especially as they are being used with increasing frequency.