Not entirely accurate. When Naruto was fighting Pain Kurama was not assisting him in the absorbsion of Nature chakra. That was all naruto.But i was right about him havin. Bijuu chakra correct? And kurama couldn't have collected that much nature energy within minutes. If that was true then Naruto would've destroyed pain with the hours of senjutsu hee had
When Naruto obtained KSM he noted that he could gather a lot more nature chakra and much quicker when Kyuubi allowed him to do so.
So Kurama did in fact absorb large amounts of nature chakra within minutes. After all he is part of the Juubi which is the Sinju tree which is Nature chakra itself.