Error warns about non-injectivity of injective type family

When I say

{-# LANGUAGE TypeFamilies, RankNTypes #-}

module Bug where

import GHC.Exts

type family F a = r | r -> a
type family G a :: Constraint

meth :: (G a => F a) -> ()
meth = undefined

I get

Bug.hs:10:9: error:
    • Could not deduce: F a ~ F a0
      from the context: G a0
        bound by the type signature for:
                   meth :: G a0 => F a0
        at Bug.hs:10:9-26
      NB: ‘F’ is a type function, and may not be injective
      The type variable ‘a0’ is ambiguous
    • In the ambiguity check for ‘meth’
      To defer the ambiguity check to use sites, enable AllowAmbiguousTypes
      In the type signature:
        meth :: (G a => F a) -> ()

The presence of G a is critical for exhibiting this bug. If I replace G a with Show a the problem disappears.

This one was actually encountered in an attempt to do Useful Work, not just idle typecheckery.

EDIT: Actually, I understand why this program should be rejected (comment:1), but the error message is surely misleading and should be fixed.