no one does natting closing their eyes, there must be a purpose why they have asked you to nat. The only reason being possible is your lan range is colliding with their existing. So they want you to nat so that the ip ranges won't clash.
FYI, it's not mandatory to use nat in your end, they can also nat and throw traffic at your end, in which case you won't be required to do anything.
This nat should not be confused with your second point. Of course you have to deny in the global nat, as usual but again have to add your exisiting hosts which requires access to vpn to nat over before the ipsec tunnel could be established and you define your vpn acl with the natted IP.
e.g if ur lan machines 192.168.1.x/24 range need access first deny them in the global nat and then put static maps with 172.16.1.x ranges and then define your vpn acl with 172.16.1.x Ip range.
so vpn concentrator would see the traffic coming from 172.16.1.x range and not ur actual 192.168.1.x range.