Absolutely untrue. There are some good relief pitchers, and there are some garbage ones, but there aren't many of them who are better than the starters they are replacing. "Fresh" does not necessarily mean 'better'. Relief pitchers are essentially there today to prolong the careers of the modern-day pampered starters, and not much else. The advent of the relief specialist is a relatively recent one in baseball history. Guys like Pedro Martinez, for example, would have had a short career if he played in the earlier days of baseball, because he's generally only good for about 6 & 2/3 innings and then he weakens and gets hit hard.
Bear in mind, if you didn't have the stamina to go the nine innings back then, you weren't going to be a major league pitcher. Also bear in mind, these pitchers who used to go nine innings were just as sharp at the end as they were in the beginning. The ability to go nine strong innings is not exactly unique to old-time baseball. Think Nolan Ryan, who threw 222 complete games. You had to be the durable, Nolan Ryan type in Ruth's day to make it as a pitcher.
Many of the 'nine inning pitchers' of years past paid the price with shortened careers, but they were great while they lasted. Sandy Koufax comes to mind. He was the most dominating pitcher in baseball in the early-mid sixties, and he pitched 27 complete games in each of his last two years. But by age 30 he was finished, because the relief specialists hadn't entered the game yet hence he burned out early. So when you mention modern-day "relief specialists", I am not impressed. With the exception of a few dominant 'closers', most of them are average, many of them are crap.
I apologize for only having data going back to 2002, but that's all that was immediately available. Data is from ESPN.com. These stats are aggregate for the entire major leagues. The 2006 numbers are totals to-date:
2002 Starter ERA: 4.41
2002 Bullpen ERA: 4.00
2003 Starter ERA: 4.52
2003 Bullpen ERA: 4.14
2004 Starter ERA: 4.62
2004 Bullpen ERA: 4.14
2005 Starter ERA: 4.36
2005 Bullpen ERA: 4.11
2006 Starter ERA: 4.66
2006 Bullpen ERA: 4.19
So, you can see a pretty clear pattern. In aggregate total, relievers reduce scoring efficiency by about 9% compared to starting pitchers.