Lots of idea's get thrown up on whiteboards where I work, but the boss man is a little paranoid. In order to become a regular user I would need to know that nothing I email over is being kept.
I understand the insecurities of email in general, but there's a difference between available for the duration of the email transmission and available for days after the email has been sent.
Thanks for being responsive.
For all of the security measures that can be taken with sending data to web applications, "never sending it at all" is very secure indeed, and in some arenas, the inconvenience may be worth it.
They almost certainly would not use the web version, unless they could run it 100% internally on their intranet.