I will assume your scanner test setup is using the same or similar antenna's to capture the traffic. Based on your video, I'm gonna wager its not intermod or a image, and its not rebroadcasting.
If it were an intermod or image, unless you were sitting on top of the transmitting unit there would be some noticeable signal degredation. Additionally, based on your monitoring of both their authorized input and the GMRS 467.725 input, if *I* were in your position without further information, I would say yes, some combination of field units and the repeater are incorrectly or sloppily programmed by whatever contractor did the work for Centereach.
My only suggestion would be to capture another series of events with *clear* traffic on 467.725, *AND* the repeated output on the 476.8625 repeater output.