tbalazs,
What they are probably insisting on is using their "network". I used to use RCN for dialup. When I got DSL some time back, it was through Verizon. Initially, I was able to get into my RCN mail with no problem. After a time, I was unable to access their servers and found out they had instituted a new policy requiring that you be on their network to access the servers. As far as I know, they are looking at the IP and subnet to verify this. If your DSL is through the same ISP, this should NOT be a problem.
While I think it is nit-picking, I can still understand the reasoning from an ISP's perspective. They don't want just anyone using their servers, especially these days with spammers, theft-of-service and virus threats. Verizon requires that the sender of an email be a valid Verizon account, so if I wanted to send an email under some personal address, it would be bounced. Many consider this to be restrictive also.
Bottom line is, it's their facility and they can protect it whatever way they feel is right. There are plenty of ISP's out there and if this one's policies seem wrong, you can always switch.
Hope that helps.
The Old Man