I've always been a bit unsure about this whole EICR thing myself. I've always been aware that it only needs to conform to the regs at the time of install but when I spoke to the elecsa man he recommended I put socket outlets without RCD as a code 1. Now, im not saying this is correct because this logic on, say a 30 year old install, would be conforming to niether the regs at time of install or the current regs (in that hes only requiring RCD on sockets and not all flushed cables) but to the 16th edition.
With regards to the OP....(ive not read whole thread so sorry if im repeating somebody else)
What you say is correct, its not required by law but it protects the landlord if the poo hits the fan. Yes you still have to pay the guy if the result is a fail, no you dont have to use him to do the remedial work.
If the house burns down, all the kids die and you end up getting investigated...if you have an EICR saying its a fail and listing the non conformities and then an installation cert from another contactor describing the rectification of said non conformities.....well...I'd say you're pretty well covered.