I found another way to set these values:
if (theDoc.GetInfo(-1, "/Info") == "")
theDoc.SetInfo(-1, "/Info:Ref", theDoc.AddObject("<< >>").ToString());
theDoc.SetInfo(-1, "/Info*/Company:Text", "ACME");
After setting the values in this way, I'm able to retrieve them like so:
if (theDoc.GetInfo(-1, "/Info") == "")
theDoc.SetInfo(-1, "/Info:Ref", theDoc.AddObject("<< >>").ToString());
string companyName = theDoc.GetInfo(-1, "/Info*/Company:Text");