That's an interesting thought process... "some warming is natural" means "no warming is artificial."
You're right of course, it's terribly flawed logic. Just as flawed as the logic in "The greenhouse effect is demonstrable in a test tube, therefore it is the primary factor directly controlling the temperature of Earth."
Real scientists don't make such simplistic and unjustified steps in their logic. Unfortunately, because real scientists remain silent when they don't have verifiable mathematics and experiment to back a theory, we only get to hear the charlatans for whom contributory data is equivalent to understanding the whole thing.
Obviously the conundrum is that if you wait to do anything until you have such proof it may be far too late to do anything about the problem. Death for everyone. On the other hand, if you take early action and there was no justification then you wasted some money. Money spent in some "green" sector vs some other one.
The "conservative" choice is clearly to treat global warming as a legitimate threat.