The study below suggests that it is true. Whether the evidence is sufficiently conclusive for the question about easier running is debatable.
Bestaven E, Guillaud E, Cazalets J-R (2012) Is “Circling” Behavior in Humans Related to Postural Asymmetry? PLoS ONE 7(9): e43861. doi:10.1371/journal.pone.0043861. Available online, open-access.
In this study, they led blindfolded people attempt to walk straight in a room without any clues. They found that, for the total number of trials, 50% trajectories terminated on the left side, 39% on the right side and 11% were defined as “straight”. Quoting from the article:
Results were considered statistically significant for P<0.05. (...) One striking characteristic is the wide variability of the trajectories; some of them reached the edge of the area (Y axis) in less than 30 m (in the X direction) while other trajectories still remained straight at 140 m. The majority (50%) of the trajectories ended on the left side, 39% on the right side and 11% were defined as “straight”
This result shows that statistically speaking, on average, people do tend to turn left more easily than right, although the variability is large. This may suggest that running in a left-hand turn (counter-clockwise) is easier than in a right-hand turn (clockwise), because the left-hand turn would — statistically speaking — be the most likely to happen among the three alternatives left, straight, or right.
As to the why, this may not be strictly on-topic on Skeptics.SE, but quoting from the abstract (emphasis mine):
Posturographic analysis, used to assess if there was a relationship between functional postural asymmetry and veering revealed that the mean position of the center of foot pressure during balance tests was correlated with the turning score. Finally, we established that the mean position of the center of pressure was correlated with perceived verticality assessed by a subjective verticality test. Together, our results suggest that veering is related to a “sense of straight ahead” that could be shaped by vestibular inputs.
So, if we believe this article, neither of the reasons you quoted is correct.
Thanks go to my secondary school Biology teacher for his claim (some time around 2002) that when people cross over a field of grass in a park (e.g. to cut off a corner), the resulting path is not straight, but slightly curved, as can be easily seen by looking at the trail; he said that this was due to the asymmetry of the human body. I found the above article by his merit.