Wikipedia defines Turing test as "a test of a machine's ability to exhibit intelligent behaviour equivalent to, or indistinguishable from, that of a human". If we want to consider chimps intelligent, then in that context the definition of the Turing test should be adjusted accordingly. My point still stands: if we want to determine whether a chimp exhibits intelligence comparable to a human, we do the original Turing test. If we want to determine whether a chimp exhibits chimplike intelligence, we test not for, say, natural language but for whatever we want our definition of intelligence to include. If we want to determine whether an artificial agent has chimplike intelligence, we do the second Turing test. Unless the agent can display as consistent an intelligence as chimps, we shouldn't conclude that it's intelligent.
Regarding your point on weak measures: If I can find an endless stream of cases of failure with respect to a measure that we care about improving, then whatever collation of weak measures we had should be null. Wouldn't you agree? I'm not against using weak measures to detect intelligence, but only as long as it's not trivial to generate failures. If a chimp displays an ability for abstract reasoning when I'm observing it in a cage but suddenly loses this ability once set free in a forest, it's not intelligent.