That stat is bit of a generalization though.
There are differences in systems that would have to be considered a variable not calculated in those numbers;
It doesn't matter -- if an underlying relationship existed, some degree of (statistically significant) correlation should emerge. But this isn't the case; for the ten years of data that have been produced, only two (2003-04 and 1982-83) showed a statistically significant correlation between shots against per game (or per minute) and save percentage. Here's the catch: the correlations were in opposite directions. There is absolutely no evidence for any enduring relationship.
for example the 4 teams with the lowest shots against/game in the NHL this season:
Chris Osgood - .914
Henrik Lundqvist -9.12
Evgeni Nabakov - .910
Marty Turco - .909
Probably four of the best goaltenders in the league, right? Better then Lehtonen, Biron, Vokoun, Backstrom, Price, Thomas and Ellis at any rate? The later list of goaltenders all have significantly higher shots/game and better save percentages.
I don't necessarily agree that those four goaltenders are among the best in the league -- it's just not something that's supported by the data.
Last year, there was somewhat of a (positive) relationship between SA/M and save percentage among goalies. While not statistically significant if only the top 30 goaltenders are sampled, if I increase the sample size to include all 44 goalies who meet the minimum shots against criteria, the correlation is significant. However, this wasn't the case for either of the other two post-lockout years, and while my chart indicates that there also was a significant positive correlation between save percentage and SA/M in 03-04, this disappears if I increase the sample size to 45. 2007-08 appears to be the exception to the rule.
You'd have to think there's a common sense argument involving high percentage shots and the elimination of low-percentage shots in a system like, say, the Dallas Stars organization? If your teammates aren't allowing shots from the outside into the crest and the ratio of good scoring chances to total shots is higher because of it, it only makes sense that a goaltenders save percentage would suffer. Even if the blanket stats don't support the argument.
Incidentally, this is true of the Stars themselves, who ranked 3rd last in the league in terms of shot quality against, yet were 4th best in shots against. The Rangers were characterized by a similar pattern, if less pronounced.
In general, though, there isn't a tradeoff between shot quality allowed and shots allowed. Alan Ryder, who annually publishes a study that - among other things - examines the issue of shot quality on a team by team basis, has this to say on the subject:
"Last year I observed that the correlation of SQA to shots on goal was very weak (r2 = .15). This year it was a bit lower (r2 = .12). This is continued evidence that shots allowed and shot quality allowed are two distinct elements of defensive ability."
It's worth noting that the correlation Ryder refers to is actually positive. Teams that had higher shot totals against were somewhat more likely to give up higher shot quality.