They can't be universally true can it? I know Hades is built on a basically in-house engine, and I think it released on all platforms simultaneously... then again that studio might not even qualify as "indie" especially now... are custom engines like that really that rare nowadays?
Supergiant games doesn't have a publisher, they publish it themselves so they can do whatever they want. I don't really consider them indie, to me "indie" is when the people developing it are also the people funding development, meaning people make choices without worrying about what others opinions.
As for self made engines, if you make it yourself then that is a risk. If you make it in unity or unreal then the publisher knows they can easily find people to help you ship it if there are problems, but for a self made engine it could be unsalvageable.
