Still better than the alternative
There might be something to your analysis, but I still find this infinitely preferable to an amoral sleazeball with an almost perfect skill at controlling his public facade. Clinton would have been keenly aware of every camera at a baseball game, and each move he made, sincere or not, would have been guided by that knowledge.
This skill, of course, is why he could--and did--look you in the eye with total sincerity, and lie in his teeth.
Sometimes he almost got caught, as with that famous footage from Ron Brown's funeral (an AVI clip can be found here.)