Install carpet tiles over laminate in basement?
Give the history you know of with the home, it's probably not a concern. I'd ask the carpet manufacturer how it affects your warranty, though. As easy as laminate is to remove, it might be worth doing. 

One drawback to the adhesive tiles--if your basement floods you can't lift the carpet to dry things and salvage it. I've been involved with several basement floods (clean water, not sewage) where we were able to lift the carpet, remove the pad where it's saturated, blow-dry the concrete and carpet, and reinstall the carpet. You can't tell it happened, and this was light-colored plush. Obviously that wouldn't be possible with glue-down tiles. Just something to consider.