Reading the PEP 572 document I don't see anything stating that Walrus operator in list indexes must be enclosed in parenthesis. 

Minimal Example: 
'''
In [1]: a = list(range(10))

In [2]: idx = -1

In [3]: a[idx := idx +1]
  File "<ipython-input-3-65fc931e77dd>", line 1
    a[idx := idx +1]
          ^
SyntaxError: invalid syntax

'''

If you enclose in parenthesis it works as expected: 
'''
In [4]: a[(idx := idx +1)]
Out[4]: 0

In [5]: a[(idx := idx +1)]
Out[5]: 1

In [6]: a[(idx := idx +1)]
Out[6]: 2
'''

Is this a bug or am I misreading the PEP 572 document somewhere? It's not a top-level assignment nor is it a list comprehension so I would expect it to work in the first example.

PEP 572 does not saw much of anything about when parens are needed.  Nor does the low priority itself.  Looking through the grammar of expressions, an assignment_expression is also a starred_expression, a positional_item (in calls), and the first part of a comprehension. It is not itself an plain expression unless and until wrapped in parentheses.  Subscription requires an expression list, which may be a single expression.

To put it another way: an expression is an assignment expression but an assignment expression with a "name :=" prefix is not an expression, so parens are required anywhere an expression is required.  That includes subscripts, slicings, displays, call items other than positional items, comprehension parts other than the initial expression (maybe, check), parts of conditional expressions (maybe, check), and lambda expression bodies.  After checking, I would like a sentence added to the doc before the 'go see the PEP' bit.

This has nothing to do with asyncio.

New changeset cae60187cf7a7b26281d012e1952fafe4e2e97e9 by Lysandros Nikolaou in branch 'master':
bpo-42316: Allow unparenthesized walrus operator in indexes (GH-23317)
https://github.com/python/cpython/commit/cae60187cf7a7b26281d012e1952fafe4e2e97e9