First off I would caution giving advise on a venting system I have never seen. Sometimes a picture is worth a thousand words.
The UPC, UMC, IPC and the IMC all require factory built vents be installed to their listing. If Ameri-Vent's listing includes an Ameri-Vent Bucket and Cap be installed anything else would be a violation of Ameri-Vents listing. Most inspectors will not call you on it but it would be a violation of the listing.
I'm not sure I understand what he has as a house vent. If it really is a chimney he may have a chimney liner. If he has B-Vent the fact that the inner liner is loose means the vent is bad and needs to be replaced. Either way it should probably not have been cut.
"Somewhere a Village is Missing Twelve Idiots!" - Casey Anthony
I never lost a cent on the jobs I didn't get!