I think this is absolutely essential that the seat is affixed to the existing seat! Sadly, in my line of work, I've seen far too many cases where seats are not fixed/wrongly fixed and the consequences have been appalling! The forces experienced in even what we may consider low speed impacts are quite remarkable. There's been other threads on chassis designs and the standard protection - even there, posters talk of never feeling quite wholly protected and therefore I'm a little concerned that peeps are not fixing seats down for young'uns...
Don't just think of front end collisions, but rear, lateral and quarter. These forces can be enough to rip a person out of a seat even when belted in. I guess a crude example to display this is, have you ever seen any of the numerous YouTube videos where a person appears to be properly strapped into a seat on a show ride (and he/she probably is to the best of the safety design), only to start slipping out due to forces during the ride!!
Chris, it's good that your seat is fixed but I wouldn't give a rat's a** if the local bobby was happy or not .. it's not his child sitting in the seat plus he's not the expert .. nor am I, but for my first hand experiences.
I also think that those peeps that are taking an approved safety seat and cuting/re-shaping/adjusting it to suit may find that their actions would be lambasted should the worst happen!