Distributions are not independent for Empirical

While the documentation states that

The first k dimensions index into a batch of independent distributions

this is not the case for the implementation.
As can be seen from this MWE, the samples for every distribution are always the same:

import numpy as np
import tensorflow_probability as tfp

a = np.random.randint(0, 100, size=1000)
dist = tfp.distributions.Empirical([a, a])
n = 3
dist.sample(n)

# output
# <tf.Tensor: shape=(3, 2), dtype=int32, numpy=
# array([[66, 66],
#        [33, 33],
#        [98, 98]], dtype=int32)>

The root cause seems to be at this location, where indices are sampled only once but re-used for every distribution:
https://github.com/tensorflow/probability/blob/fbc5ebe9b1d343113fb917010096cfd88b32eecf/tensorflow_probability/python/distributions/empirical.py#L236-L238

I now fear that there might be more issues in the implementation of Empirical, rendering it unusable in contexts where I require independency between distributions.

Also the shaping of the output seems strange, which is (n, k), while I would expect it to be (k, n).

Maybe I also completely misunderstood the documentation.

Start with tensorflow_probability/python/distributions/empirical.py at the referenced lines 236-238, then run the Python MWE to inspect how samples are produced for batched Empirical distributions. Check the documented independence and output-shape expectations against the observed results; done means the behavior and its tests agree with the documentation.