mail() function returns TRUE but no email is sent

Anyone run into this problem before? I've got a simple email parser that I've set up for our clients to access from their websites. It just uses the simple mail() function to send the parsed HTML to their account. The mail() function is returning TRUE but the email no email is being received. How does the mail() function check if the email has actually been sent? Is it possible that the mail() function could be given the proper signals to return TRUE but then the server not send the email? Thanks, Kevin