For me, the differences are that those examples quoted were for solo albums. Who he works with is vs who he tours with is of limited interest. However, if I'm buying a record by Crowded House, I expect Crowded House to have recorded that record. I'm not bothered by the odd instance of "outside help" and I don't expect the band to have played on every song. Never said I was.
The issue isn't one of "how many band members played on each song". It's about the intent. As I noted above, Beautiful Night has more Beatles on it than Yesterday but no one (no, not even me) would consider it a Beatles record because it wasn't recorded to be a Beatles record and the two Beatles who are on it performed in their capacity as solo artists not members of that band.
This is also the case with TOE. It was recorded by Neil as a solo artist with Nick playing bass as a session man/collaborator but neither felt they were acting as members of CH and there was no intent to make a CH record.
I don't think anyone here would describe any of the line ups that recorded the core of Time on Earth (that is, the songs that were recorded before the band reformed) as being Crowded House. Of course, where one draws the line is subjective and I understand why anything with the core of Finn/Seymour would be acceptable as CH to some.
It raises the question of what constitutes a band: for my money (and I suspect, Neil's) the heart and soul of CH was lost when Paul quit in 94. Personally, I was prepared to accept that a band comprising Neil, Nick and Mark could legitimately continue as CH and, I guess, if Mark had bailed at some point and Neil had recruited again, it still would have been CH. But would an act comprising Neil and Nick with random session players coming and going have been CH? Personally, I'd have said no.
All I can reiterate is that I have a hard time accepting an album that was recorded by Neil as a solo album being considered a band album. It just seems disrespectful to the idea of CH as a band. It basically suggests that Neil could work with whoever he wanted to and call the resulting album a CH album.
Clearly, I'm too emotionally attached to the idea of the band.