My concern goes back to the data that would have generated the graph. Certainly if the EXACT curve is a Gaussian with a mean of exactly 3.8675309 and a standard deviation of exactly 0.1, then plotting the exact curve will give the best fit.
But in "real life" we would never know the curve ahead of time. To get such a curve experimentally, you would measure many individual values. Then you would estimate the center. And the standard deviation. And the uncertainty of the center. And the uncertainly of the standard deviation. And whether the data is truly Gaussian.
Getting such a smooth curve experimentally would take a HUGE number of data points -- let's say 10^10. Then the uncertainly of the mean would be around 0.1 / (10^10)^0.5 = 0.000001. The error in the standard deviation is also of order N^-0.5. So you are really illustrating something more like "A distribution with a mean of 3.8675309(10) and a standard deviation of 0.100000(1)"
If you generate only 100 or 1,000 points randomly from the appropriate distribution, I suspect you would have a hard time telling which fit the data better.