To be sure that I get the question right. What you are saying is, that n+random.gauss(0,noise) is not the same as random.gauss(n,noise)?

I checked the implementation of gauss (python 2.7) in random.py:

def gauss(self, mu, sigma):
"""Gaussian distribution.

mu is the mean, and sigma is the standard deviation.  This is
slightly faster than the normalvariate() function.

Not thread-safe without a lock around calls.

"""

# When x and y are two variables from [0, 1), uniformly
# distributed, then
#
#    cos(2*pi*x)*sqrt(-2*log(1-y))
#    sin(2*pi*x)*sqrt(-2*log(1-y))
#
# are two *independent* variables with normal distribution
# (mu = 0, sigma = 1).
# (Lambert Meertens)
# (corrected version; bug discovered by Mike Miller, fixed by LM)

# Multithreading note: When two threads call this function
# simultaneously, it is possible that they will receive the
# same return value.  The window is very small though.  To
# avoid this, you have to use a lock around all calls.  (I
# didn't want to slow this down in the serial case by using a
# lock here.)

random = self.random
z = self.gauss_next
self.gauss_next = None
if z is None:
    x2pi = random() * TWOPI
    g2rad = _sqrt(-2.0 * _log(1.0 - random()))
    z = _cos(x2pi) * g2rad
    self.gauss_next = _sin(x2pi) * g2rad

return mu + z*sigma

As you see, mu is added at the end, so there is basically no difference between n+random.gauss(0,noise) and random.gauss(n,noise). If I misunderstood your question, then please clarify

I can't see how it can be better?

2000 runs is probably not enough.

Changing the mean of a Gaussian just seemed to move its graph along the x axis, the shape of the distribution was the same. So you'd expect if random.gauss(0, 5.0) is returning +/- 25, say, that (50, 5.0) will return 25 to 75.

As for the real world, "it depends" is probably the best answer.
But intuitively you might expect that the further you went, the bigger the error would be. So this +/- 25 regardless of distance seems unlikely.

But in the real world your robot or car isn't likely to travel large distances without a sense and resample step in any case. So it might be that at road speeds with typical sensing and resampling rates it works.

In my point of view they are exactly the same. I wouldn't say that 4% difference is a conclusive result. If you try running the test again (2000 more times) maybe you will get inverted results.