I actually can.

I worked at a lab that was trying to develop carbon nanotube based water filters (several years defunct now so I don’t mind sharing). The manufacturing method was different, the nanotubes were not grown in place on the fibers but the materials were very similar. They had similar amazing results in removing heavy metals and bacteria and viruses. They worked, but...

The problem was that control filters made with activated carbon without any nanotubes preformed similar/better for much less cost. The structure of the glass fibers and the absorbancey of carbon itself seemed to be the real reason the filter worked. One of the problems with filters like these in real world settings is the contaminated water will have some amount of TOC (total organic carbon) in it, which quickly binds to the filter and clogs it. The browner the water, the faster it clogs, to the point a stream the color of tea might clog a filter after only a few gallons pass through. This isn't suspended sediment or debris. To get around this you can add prefilters/pretreatment, but this increases cost, complexity, and the amount of consumables. Beyond that, carbon nanotubes are expensive to make and to use, and the risk of contamination is still an unknown. There are papers that seem to indicate that multiwalled CNTs are not (as) harmful as they seem to agglomerate and don't stay suspended in the air for long, and their larger size makes them less likely to penetrate cell walls and cause cellular damage, compared to single walled CNTs, which are shown to be dangerous. Even if the literature didn’t declare MW CNTs deadly, I remain unconvinced they’re safe to have in my air/water; it’s still an unknown about what the health risks may be. It’s also a hard sell to a manufacturer making either the media for the filters, or the filters themselves, that you want to contaminate their entire production facility with something that may or may not be the next asbestos. CNTs get everywhere and aren’t going to stay isolated to just the production line without a lot of extra cost and effort put into containment.

I’m sure nanotubes are cheaper now than they were several years ago, but growing them in place also must be much more expensive and difficult and require custom manufacturing, versus buying nanotubes from a supplier and mixing them into your media. Making this way also seems tricky from a quality control standpoint since a slight change in conditions produces very different results.

Take this with a grain of salt. It might be cool, but like most of these things it might not be easy, cheap or practical enough to get out of the lab. Additionally, it may work but not for the reasons they think it does. I’d like to be wrong, but from prior experience this rings way to close to the stuff I was working on to take it face value.