Questioning win rate confidence intervals

[Girchuck]

Lets say that you are a 3BB/100 winner over 25K hands.
If you estimate a 95% confidence interval of your true win rate, it would be approximately from 1 to 5 BB/100
However, in real life there are many more 1BB/100 winners than 5BB/100 winners. Intuitively, I think that 5BB/100 true win rate is less likely for a player with the above stats than 1BB/100 win rate. In other words, I doubt that the Gaussian distribution is unbounded on the right side.
Am I in error?