I think that, for the sort of cases outlined below,
CheckUser could
be used perhaps if the user themselves specifically said it would be
OK.
ROTFL! It means that we should ask every sockpuppet for permission to
check to see if he is a sockpuppet. :-D
If the sockpuppet is denying that it is a sockpuppet,
it should be willing to give permission, ne?
Not necessarily. Someone wrongly accused of being a sock puppet could
well have objections to an IP check on grounds of privacy.