I hate to say it, but I think you are both right
That command (nor many others I find listed for XP command prompt) will not run on my XP Home systems and I receive the error message OP noted.
OP is correct in saying that the command should run...according to every list of command prompt commands which I have looked at for XP.
I have no explanation for this...other...wait, I think I see the problem.http://commandwindows.com/tasklist.htm
"This tool is part of the regular installation of the Professional version of XP but does not come with the Home edition. However, those with the Home version of XP can download Tasklist here
Sooooo...for users of XP Home, they should expect to receive the error message indicating it is not a valid command (unless they have taken steps to install same in XP Home).