He's a liar (or at least flat-out wrong). There were no more than 9.
Here is Utah's draft history from nfl.com:
http://www.nfl.com/draft/history/fulldraft?collegeName=Utah&abbrFlag=0&abbr=U&type=school
They had 5 players drafted in 2005, and 2 each in 06 and 07.
Also, I don't know that Weddle and Soliai were starters as sophomores. Even if they were both starters, that still gives them only 9 starters (which is still impressive, IMO).
On the flip side, our 1980 team had 11 players drafted.
Our 1985 team had 14 players (not necessarily starters) drafted in the 86-88 drafts.
Nevertheless, I don't think NFL draftees is a good indicator of a team's strength.