They only have your outbound mail (which admittedly may include quotes from inbound mail), and are (ostensibly) not storing it long-term.
I've been running a split setup like this for a year or two. I found that my free-with-apartment internet connection, amazingly, gave a fairly static IP (it was DHCP but usually the same) and unfirewalled inbound ports, so I set up a mailserver for inbound mail and IMAP storage. I figured the IP might be on anti-spam blacklists, firewalled on port 25, or shut down if the ISP saw me mailing out, so I sent outbound mail through Dreamhost. It was nice to have the full copy of my mail in my house, with backups and spam filtering under my control. Sending outbound through a 3rd party wasn't ideal, but I thought a decent compromise to avoid having to talk to the ISP and risk the free public IP being taken away (I wouldn't have even known who to contact anyway.)
As a bonus, I set the Dreamhost mail server as a backup MX with the same email address I host myself, so they catch mail for me if my server or connection goes down.
I now have official "small business" ISP service that includes several public IPs, so I am transitioning to sending my own mail, now that it's definitely kosher and I'll have support.
I've been running a split setup like this for a year or two. I found that my free-with-apartment internet connection, amazingly, gave a fairly static IP (it was DHCP but usually the same) and unfirewalled inbound ports, so I set up a mailserver for inbound mail and IMAP storage. I figured the IP might be on anti-spam blacklists, firewalled on port 25, or shut down if the ISP saw me mailing out, so I sent outbound mail through Dreamhost. It was nice to have the full copy of my mail in my house, with backups and spam filtering under my control. Sending outbound through a 3rd party wasn't ideal, but I thought a decent compromise to avoid having to talk to the ISP and risk the free public IP being taken away (I wouldn't have even known who to contact anyway.)
As a bonus, I set the Dreamhost mail server as a backup MX with the same email address I host myself, so they catch mail for me if my server or connection goes down.
I now have official "small business" ISP service that includes several public IPs, so I am transitioning to sending my own mail, now that it's definitely kosher and I'll have support.