It's also important to ask the author of the site, or at the very least check the metadata to make sure that they allow this use of the data. For example, since I work for a nonprofit our map services can't be used in a for-profit web map without getting specific permission. Some other groups have more restrictive licenses (where you can only access the data via a specific site), and even if they don't prevent you from working around them they should still be respected.
Thanks for noting the considerations required. The WMS is public, and is available to be consumed. The REST Endpoint of the same map service as ArcGIS REST is public as well, although the meta is not provided.