I agree with the 3.3% probability of having 3 or more solutions, but that does not mean that there is something more going on here.  1 in 30 chances occur all the time.  If you roll a pair of dice and they come up snake eyes, would you conclude that they are unfair dice, just because the probability of snake eyes is 1/36?  I think that 3 squares that fit the pattern is well within the realm of possibility.