I was going to delete this, but I'll leave it up in case someone else has the same problem. Here's the solution -- the call to Documents.Open has to have more arguments. The MS documentation says they're optional, but there are side-effects to not providing them.
var wordApp = new Microsoft.Office.Interop.Word.Application();
wordApp.Visible = false;
Document wordDoc1 = wordApp.Documents.Add();
Document wordDoc1a = wordApp.Documents.Add();
Document wordDoc2 = wordApp.Documents.Open(@"c:\users\robertsf\desktop\doc2.docx",
false, false, false, "", "", false, "", "", WdOpenFormat.wdOpenFormatAuto,
MsoEncoding.msoEncodingUTF8, false, false, none, none, none);
Now it works as expected. I haven't experimented to see exactly which argument caused the issue.