I've never heard of a storm box built with CMU, but I have heard of manholes built of brick. I've always seen manholes and boxes either made from precast concrete or cast in place. I can't imagine the costs are that significant over this CMU idea. (Contractor probably has a stockpile of it from his last masonry job)
I would be inclined not to allow this if possible, or at least require them to get an engineer to sign off on the design. How deep is the box, and is it in a traffic area recieving loads? If so you could say this is a health and safety issue.
I am not sure the CMU blocks, or the grout between them, will hold up that well against water erosion. I think the CMU blocks are only constructed with fine aggregates which might make it susceptible to eroding.
Lastly, you mentioned this is a private storm system..are you sure? For example will the storm system convey any off site flows, if so it should be considered public with an easement for the other neighbor.
Also, will this system discharge into a public storm system or drainage course (of course it does eventually), then you could claim their design doesn't mesh with the standards of practice in your area.
Is there high groundwater? Make them do a vacuum test, hehe, it will never pass.