Thanks for the extra details Mr^B - I'm going to have to do so reading up on what it really means to override a method - while I get the idea, I don't know what it means yet, if that makes any sense. Basically, I think I definitely qualify as a garden app maker for the moment 
In case any one else comes across this post in the future, I've taken this snippet of code one step further, by making my Master Page "strongly typed" for the .aspx pages that use it - basically, the code below, in the master page's code-behind file, allows me to access the authenticated user name and group name within each page that uses the master page. More on how to do this here: http://msdn2.microsoft.com/en-us/library/ehszf8ax(VS.80).aspx
Any page that uses the master page must use this tag at the top (I guess that this lets the .aspx page inherit the master page properties & methods (which is added below) ?):
<%@ MasterType VirtualPath="~/MasterPage.master" %>
With the above line, now my .aspx file can use Master.strNameUser and Master.strNameGroup to get the values set in the Master Page - definitely something pretty basic for .NET or OOP coders, for this Classic ASP kid, this was a major breakthrough 
Here is the new code for my master page:
1 public partial class AppName_MasterPage : System.Web.UI.MasterPage
2 {
3 // Allows any page using this Master Page access to the currently
4 // Logged in User's Basic Authentication Name (logic in Page_Init below)
5 public String strNameUser
6 {
7 get { return (String)ViewState["strNameUser"]; }
8 set { ViewState["strNameUser"] = value; }
9 }
10
11 // Allows any page using this Master Page access to the currently
12 // Logged in User's Basic Authentication Group (logic in Page_Init below)
13 public String strNameGroup
14 {
15 get { return (String)ViewState["strNameGroup"]; }
16 set { ViewState["strNameGroup"] = value; }
17 }
18
19 // Set the strNameUser and strNameGroup properties above based on the
20 // user that has logged in with Basic Authentication
21 void Page_Init(Object sender, EventArgs e)
22 {
23 // Set the Logged in User Name Property of this
24 // strongly-typed MasterPage
25 this.strNameUser = HttpContext.Current.User.Identity.Name;
26 lblNameUser.Text = this.strNameUser;
27
28 // Set the Logged in User Group Property of this
29 // strongly-typed MasterPage
30 if (HttpContext.Current.User.IsInRole(@"COMPUTERNAME\GROUP1"))
31 {
32 this.strNameGroup = "Group 1";
33 lblNameGroup.Text = this.strNameGroup;
34 }
35 else if (HttpContext.Current.User.IsInRole(@"COMPUTERNAME\GROUP2"))
36 {
37 this.strNameGroup = "Group 2";
38 lblNameGroup.Text = this.strNameGroup;
39 }
40 }
41
42 // Transfer the user away from the page if they haven't logged in
43 // (Basic Auth shouldn't let the get that far but..) or if they
44 // have logged in, but don't belong to a specified user group on
45 // the server.
46 protected void Page_Load(object sender, EventArgs e)
47 {
48 // Please note that if the page you're transferring to on
49 // lines 55 and 59 below (unauthorized.aspx) is using this master
50 // page, IIS will crash (will begin looping) - make sure that
51 // the page you transfer to uses a different master page
52 // or none at all to avoid this problem.
53 if (HttpContext.Current.User.Identity.IsAuthenticated == false)
54 {
55 HttpContext.Current.Server.Transfer("unauthorized.aspx?msg=user");
56 }
57 else if ((HttpContext.Current.User.IsInRole(@"COMPUTERNAME\GROUP1") == false) && (HttpContext.Current.User.IsInRole(@"COMPUTERNAME\GROUP2") == false))
58 {
59 HttpContext.Current.Server.Transfer("unauthorized.aspx?msg=group");
60 }
61 }
62 }
Best,
Darin