Interesting.

Okay, the first two credits say "under section 151 is allowable to another taxpayer".  So I agree, if the parents' don't live in one of those countries (but the OP did not say where they live), it would not be "allowable" under Section 151 for the parents to claim the child.  So yes, the child could claim the credits (again, that is only *IF* the parents are not in one of those countries that would allow claiming a dependent).

However, the third credit is different.  It says "any individual who is a dependent of another taxpayer ... For purposes of this section, the term “dependent” has the meaning given such term by section 152."

To me, Section 152 means if the child meets the dependency test, regardless if the parents are able to claim the child.  If that is the case, the child would not qualify for the third credit.