Normally cardboard that does not have a wax coating, or is not covered with some ink based writing or coloring is generally safe and digestible. Quoting Dana Krempels "As long as the paper and cardboard have no print containing heavy metals (as many colored inks do), there is no harm in your bunny eating it. Paper is made of cellulose, which is digestible to rabbits."
And of course, you don't want your bunny filling up on paper and forgoing his diet, that would be what you need to really watch out for more than anything.
HOWEVER, you bring up something to think about regarding the cement tubes. IF what he is saying is a bunch of junk is mixed in the recycled paper to make the tube, then that would be concerning!