That exact shape is already one of the reasons Profile A sanitizes the Git subprocess environment.
The answer to your last question is: neither.
Profile A does not build a minimal environment from scratch, but it also does not inherit the caller environment and assume the Git variables are clean. It copies the inherited environment and explicitly removes the Git Authority/config override surfaces before the Git subprocesses that establish or consume local Authority.
That includes:
GIT_DIRGIT_WORK_TREEGIT_INDEX_FILEGIT_COMMON_DIRGIT_OBJECT_DIRECTORYGIT_ALTERNATE_OBJECT_DIRECTORIES
plus GIT_CONFIG_COUNT and indexed GIT_CONFIG_KEY_n / GIT_CONFIG_VALUE_n.
GIT_INDEX_FILE specifically is there because I reproduced the same property earlier: explicit --git-dir and --work-tree do not override it, so a foreign index can otherwise substitute the tracked-path set after the nominal git-dir has already been qualified.
In the current Profile A implementation, both Git subprocess call paths use the same _git_authority_subprocess_env() helper: the final git ls-files --sparse -z call and the git config --local calls used during Authority qualification. So qualification and consumption use the same environment-isolation policy.
There is also a regression test for the GIT_INDEX_FILE case, and I kept it after switching the final query to --sparse, specifically to make sure this hardening did not regress.
Your witness does add a useful general point, though:
clean rc + clean stderr + supported output representation
!=consumer used the qualified Authority
In this case there is nothing in the consumer's result channels that can tell us afterward which index Git actually read. The foreign one-entry index produces a perfectly plausible successful answer.
So this is another case where trying to infer Authority from the consumer's output is too late. The Authority-selection surface has to be constrained before the consumer runs.
That is also why I treat environment sanitization as part of Authority binding rather than as output validation.