site.getusersitepackages() incorrectly claims that PYTHONNOUSERSITE is respected

[pelson]

BPO	41376
Nosy	@methane, @pelson, @pablogsal, @miss-islington
PRs	bpo-41376: Correct the documentation on site.getusersitepackages() regarding respecting PYTHONNOUSERSITE #21602 [3.9] bpo-41376: Fix the documentation of site.getusersitepackages() (GH-21602) #22591 [3.8] bpo-41376: Fix the documentation of site.getusersitepackages() (GH-21602) #22592

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = None
closed_at = <Date 2020-10-11.18:35:11.130>
created_at = <Date 2020-07-23.15:22:11.754>
labels = ['3.8', '3.9', '3.10', 'docs']
title = 'site.getusersitepackages() incorrectly claims that PYTHONNOUSERSITE is respected'
updated_at = <Date 2020-10-11.18:35:11.129>
user = 'https://github.com/pelson'

bugs.python.org fields:

activity = <Date 2020-10-11.18:35:11.129>
actor = 'pablogsal'
assignee = 'docs@python'
closed = True
closed_date = <Date 2020-10-11.18:35:11.130>
closer = 'pablogsal'
components = ['Documentation']
creation = <Date 2020-07-23.15:22:11.754>
creator = 'pelson'
dependencies = []
files = []
hgrepos = []
issue_num = 41376
keywords = ['patch']
message_count = 4.0
messages = ['374139', '378215', '378219', '378444']
nosy_count = 5.0
nosy_names = ['methane', 'docs@python', 'pelson', 'pablogsal', 'miss-islington']
pr_nums = ['21602', '22591', '22592']
priority = 'normal'
resolution = 'fixed'
stage = 'resolved'
status = 'closed'
superseder = None
type = None
url = 'https://bugs.python.org/issue41376'
versions = ['Python 3.8', 'Python 3.9', 'Python 3.10']

[pelson]

The documentation for site.getusersitepackages() states at https://docs.python.org/3.10/library/site.html#site.getusersitepackages:

Return the path of the user-specific site-packages directory, USER_SITE. If it is not initialized yet, this function will also set it, respecting PYTHONNOUSERSITE and USER_BASE.

Yet the implementation does not agree:

$ python  -c "import site; print(site.getusersitepackages())"
/home/user/.local/lib/python3.7/site-packages

$ PYTHONNOUSERSITE=1 python -c "import site; print(site.getusersitepackages())"
/home/user/.local/lib/python3.7/site-packages

(same result for -s and -I flags)