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This section could be clearer imho.
First of all there's nothing special about "nested" list comprehensions. In [expr for elem in seq], expr might be any expression -- including a listcomp. As with any other expression, the nested listcomp will be executed for each elem in seq, so there's really nothing new to explain here.
The "reading order" is always from left to right, with the expression at the end:
 [expr for x in seq1 for y in seq2 for z in seq3]
 ^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^^^ ^^^^^^^^^^^^^
 last first second third...
So I agree that "To avoid apprehension when nesting list comprehensions, read from right to left." is a bit confusing/wrongish (is actually correct for listcomp with only a single for, but that's just a coincidence and it's not related to nested listcomps).
The previous section could also be a little clearer, showing the classic example:
 squares = [x**2 for x in range(10)]
and saying that it's equivalent to
 squares = []
 for x in range(10):
 squares.append(x**2)
and, similarly, that
 combs = [(c1, c2) for c1 in 'abc' for c2 in 'xyz']
is equivalent to
 combs = []
 for c1 in 'abc':
 for c2 in 'xyz':
 combs.append((c1, c2))
Showing the "reading direction" with these two equivalents and saying that nested listcomps follow the same rule (because there's nothing different about them), should be enough to make things clear.
In addition, the example with the matrix shouldn't use print in the "expanded" version, but rather something like:
 res = []
 for i in [0, 1, 2]:
 res.append([row[i] for row in mat])
 print res