The main point here is that, whether the license is permissive, weak copyleft or strong copyleft doesn’t make any practical difference if the software is used to run an online service as, unless the license is one that specifically addresses the “service provider loophole” such as AGPL or CPAL, hosting the service is not considered “distribution”, therefore the conditions of the license don’t come into play at all.

(ASL is permissive rather than weak copyleft, however you are right to say that the permissive nature of the ASL does mean that downstream modifiers are at liberty to not contribute back code even where they do distribute binaries.)

‘they are at liberty to make significant changes to the software without contributing this back to the community developing the core codebase. This is because, under the terms of most open source licenses, providing an online service using software is not considered “distribution” of the software.’

If you were talking about AGPL versus GPL, this quote would be right on. But you were talking about ASL, in which case it has nothing to do with whether the software is being “distributed”. Vendors can distribute modifications in binary only form because ASL is a weak copyleft. In fact the GPL is one of the only licenses where this distinction matters at all, which is exactly why AGPL exists alongside it.