Let’s start with the sentence in question, from the December 2016 Scientific American, page 46:
Planetary scientists such as me have pieced together this new, three-ring circus version of the active young solar system with great help from new tools for calculating the ages of meteorites, as well as the ages of planetary dust clouds—similar to our primordial solar system—elsewhere in the cosmos.
That “me” in the first line doesn’t sound quite right, does it? You definitely don’t say “me have pieced together.”
Well, “me” is correct! First, figure out the actual subject of the sentence. The subject is “scientists.” So planetary scientists have pieced together all that stuff.
Still, why “me”? “Such as” is a preposition, equivalent to “like,” or “with.” So “me” is the object of the preposition. It just happens to sit next to the verb, and that proximity creates the disconnect.
Rule of thumb: Pay attention to what you’re writing.