The above statement can be evaluated by looking at how well regular season results predict playoff success. This can be done by assigning a theoretical win probability to every playoff team based on how it performed during the regular season, and determining the odds for each individual matchup on that basis. If the statement is true, the favorite - the team with the superior win probability as against its opponent - should win significantly less often than expected.
My sample consisted of all 1882 playoff games played between 1988 and 2010. Theoretical win probabilities were computed on the basis of regular season goal ratio, corrected for schedule difficulty. While goal ratio is imperfect in this respect, the data required to produce more precise estimates is simply not available for the majority of the seasons included in the sample. Thus, goal ratio is the best measure available.
Home advantage was valued at +0.056, this being the difference between the expected neutral ice winning percentage of home teams (0.505), and their observed winning percentage over the games included in the sample (0.561).
After computing the odds for each individual game, I divided the data into eight categories. The category in which a game was placed depended upon the expected winning percentage of the favorite. The cutoffs for the eight categories were as follows:
[The italicized 'n' column simply indicates the number of games contained within each category.]
As can be seen, using regular season data allows one to predict the results of groups of individual playoff games with surprising accuracy. On the whole, the favorite did slightly worse in reality than what the regular season results predicted - 0.573 versus 0.586. However, this is probably just a reflection of the fact that regular season goal ratio is the product of both skill and luck, and that the true talent goal ratio of the average team lies closer to the population average than does its observed goal ratio.
As for the individual categories, six of the eight show a reasonably close correspondence between expected and observed winning percentage, with the other two featuring notable discrepancies. While each gap appears significant, either could be the product of chance alone. The probability of a 0.51 team going 0.468 or worse over 263 games is 0.097. Likewise, the probability of a 0.713 team going 0.671 or worse over 204 games is 0.109.
If I were to guess, I'd say that the discrepancy in the 0.675-1 category is a real effect. As discussed earlier, goal ratio tends to overvalue the favorite and underrate the underdog, and the greater the distance from the mean, the more likely this is to be true in individual cases.