Sharing catalogs between multiple computers is not supported and is not an intended use case. The reintegration is there for when the catalog is moved to a different computer or re-located, so reintegration when moving a catalog between computers is expected. Yes, even if your files are still on the same drive, it may appear that the files have the same path on both computers, but this is not necessarily the case at a lower-level.
When files are offline, they are read-only. The Catalog does not support updating metadata to offline files.