In response to a conversation on Twitter, and after being introduced to the conversation by Glenn Gabe, Google’s John Mueller confirmed that Google does not index parts of a specific page independently:
We don’t index parts of a page independently, we index the pages as a whole, and try to understand the context of the content there. Scrolling to a part of a page when we know that’s where the snippet was from makes a lot of sense regardless of indexing.
This is no real surprise, as most people already believed that Google indexed either pages in full, or not at all. Though it is still useful to receive this confirmation from John.