You're correct on all counts, but the key point you're missing...

You're correct on all counts, but the key point you're missing is relevance. Keeping project costs low and getting things done quickly are existential for AGY. For RIO, their project is almost completely inconsequential. If RIO announced tomorrow that they too were placing their Rincon operation into C&M, I'm certain that it'd barely register a blip on their chart. For AGY, it's resulted in market cap decimation, with the share price down around 50% since announcing C&M.

If AGY were in a competition for who can get reach production first, or who can keep their CAPEX spend the lowest, then I'm sure we could arrange a couple of first place ribbons to be mailed to their head office. However, they should also be recognised for "fastest ASX brine operator to enter care and maintenance" and "first ASX brine operator to unsuccessfully commission a commercial plant".

The point here is that doing this quickly and cheaply isn't commendable when all it got you was a rushed and poorly executed operation that now seems to require a complete and costly re-design that cannot be achieved with available funds. Meanwhile, RIO have steadily been building out their infrastructure (including things like accommodation and an airport ahead of the full-scale operation), with first production on track for later this year.

On the CAPEX front, again it's completely irrelevant. RIO is the world's second-largest miner, with a market cap >$100b and who just generated >$7b in cash in the last 6 months. They can spend as much as they like at Rincon, whereas AGY had to cease operations due to running out of capital.

The moral of the story here is that your points only carry value in the land of HC pissing contests. Out in the real world, one tiny project with questionable viability has been placed into C&M with a fair chance it will never see the light of day, while the other, owned by a global mining giant, continues to progress on track to production later this year.