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I'm trying to read in all input cells in a notebook that are contained in (or outside of) a specific group.

NotebookImport[nb, "Input" -> "InputText"]

gives the input text of all the input cells in the notebook, but I don't know how to filter out the input cells in a CellGroup with a specific title.

A motivating application would be trying to import the input cells in a documentation notebook from only the Basic Examples and Possible Issues sections.

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NotebookImport doesn't support it directly but you could import "Input"|"ExampleSection" and just split by style. You could but you can't because somehow ExampleSection style in those cells is put there twice:

Cell[
  TextData[{"Basic Examples",... }], 
  "ExampleSection", "ExampleSection",...
]

Which is not a problem but NotebookImport doesn't support it (which is a bug imo).

So at the end we have to live with NotebookGet or Import and parse it:

Cases[
  NotebookGet[nb],
  {
     c : Cell[
       _?(! FreeQ[#, ("Basic Examples" | "Possible Issues")] &), 
       "ExampleSection", 
       ___
     ], 
     r___
  } :> (
    c[[1, 1, 1]] -> Cases[
      {r}, cell : Cell[_, "Input", ___] :> First @ FrontEndExecute[
         FrontEnd`ExportPacket[cell, "InputText"]], ∞]
  ),
  ∞
]
{"Basic Examples" -> {"nb = CreateDocument[{TextCell[\"project \
title\", \"Title\"], 

      TextCell[\"first section\", \"Section\"], 

      TextCell[\"details\", \"Subsection\"], 

      ExpressionCell[Defer[2 + 2], \"Input\"], 

      TextCell[\"second section\", \"Section\"], 

      ExpressionCell[Defer[3 + 3], \"Input\"], 

      ExpressionCell[Defer[1/0], \"Input\"]}, 

     WindowMargins -> {{Automatic, 0}, {Automatic, 0}}, 

     WindowSize -> {500, 600}];

  NotebookEvaluate[nb, InsertResults -> True];", 
   "NotebookImport[nb, _]", "NotebookImport[nb, _ -> \"Text\"]", 
   "NotebookImport[nb, \"Input\"]", 
   "NotebookImport[nb, \"Input\" -> \"InputText\"]", 
   "NotebookImport[nb, \"Input\" -> \"InactiveExpression\"]", 
   "NotebookImport[nb, \"Input\" | \"Output\", \"FlattenCellGroups\" -> \
False]", "NotebookImport[nb, \"Input\" | \"Output\" -> \"InputText\", 

   \"FlattenCellGroups\" -> False]"}, 
 "Possible Issues" -> {"NotebookImport[Notebook[{Cell[\"2+\", \"Input\
\"]}], 

   \"Input\" -> \"HeldExpression\"]", "2+", "2+", 
   "NotebookImport[Notebook[{Cell[\"Grid[{{1,2},{3,4}}]\", \
\"Input\"]}], 

   \"Input\" -> \"HeldExpression\"]", "InputForm[%]", 
   "NotebookImport[Notebook[{Cell[\"Grid[{{1,2},{3,4}}]\", \
\"Input\"]}], 

   \"Input\" -> \"InputText\"]"}}
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