That doesn't surprise me too much, I was hoping it might have caught something though.
I would normally say if you use web mail viewed through your browser then you don't need the Internet Mail provider as this doesn't scan web based email only email through a pop3 email client like OE, Thunderbird, etc.
I'm still at a loss as to what/why something would be trying to access the memory on shutdown, as I see no reason why ashMaiSv.exe would need to access memory, more so because you aren't using an email client.
All I can suggest is monitoring the situation to see if it happens at every shutdown if it doesn't cause a problem I wouldn't be unduly concerned. You could terminate the Internet mail provider then ashMaiSv.exe wouldn't be running to require memory access.
However, with the Internet Mail set to High sensitivity it can provide a useful function of detecting if your system is sending out spam, too many identical emails in a short period. You don't have to have an email client on your system as some trojan spambots come with their own very small smtp routine. So that decision would have to be yours.