I think both points are false.

Space mining companies currently have two or three possible products they usually talk about: platinum group metals, helium 3, and water.

Helium 3 would come from the lunar soil. The problem is that it is EXTREMELY rare in the lunar soil, so you'd have to process ridiculous amounts of it. It is ostensibly used as a fusion fuel, but it's actually a tougher fuel to use than deuterium/tritium, and no one has even made D/T fusion breakeven, yet. The only real advantage is that helium 3 produces fewer neutrons than D/T does. But Protium-Boron11 produces even less. And you can make Helium 3 by just making Tritium and letting it decay. So Helium 3 isn't a real market.

Platinum group metals are supposed to be this huge market. But the total value of the platinum market (and the vast majority of the PGM market is platinum by value) is just $5 billion per year. The global commercial space telecom market is already on the order of $100 billion per year. And even here, processing platinum in orbit is a HUGE technical challenge. It's in relatively small concentrations (though perhaps still better than Earth), it's not like there's a big chunk of platinum that you just need to grab.

And water. Water is supposed to be the huge, near-term space commodity. $10,000 per kilogram, "The oil of space." ...except the only current market for water is on ISS, where it is occasionally delivered by Dragon, Progress, and Cygnus. Water is not used for propulsion for any current satellites; instead, they use hydrazine, xenon, or a bipropellant hypergolic combination (usually including hydrazine).

The only other use is for upper stage propellant. But that'd require splitting the water, refrigerating the resultant gases, storing them in deeply cryogenic conditions, then delivering them to the upper stage. This is all possible, but that is only good for a small part of the trip to orbit, the part from LEO to GEO. But the starting assumption of water being super expensive is based on a faulty assumption that launch costs will remain really high, i.e. that reusable rockets won't work. If Falcon Heavy works, the cost to orbit is only like ~$1000/kg to LEO. And if BFR works (first orbital test as early as 2021/2022), costs could be as low as $10/kg. So you have to assume reusable rocketry isn't really viable. But to get water from, say, the Moon requires a reusable launch infrastructure of some kind, usually a reusable lunar lander/ascender. And usually, in order to be cost effective, it has to be totally autonomous. So you're assuming fully autonomous, refurbishment-free launch from the Moon is going to be cheap to develop but reusable rockets on Earth won't. And you're also necessarily assuming that space market growth won't be buoyed by much cheaper space launch, so you're looking at a small part (upper stage propellant) of a relatively small market (the current space launch market, which is a tiny fraction of the space telecom market). And you have to build a bunch of infrastructure on the Moon and in Earth orbit to make it work, it'll probably take over a decade to get working... Why not just invest in reusable rockets on the Earth first?

So I feel like the business case for water mining also doesn't make any sense, in spite of the difference in delta-v needed to reach orbit.

(The caveat to this is if you have a Moon base or something... in which case you already have a need for water on the Moon itself and much of the infrastructure already in place. That is reasonable, IMHO.)

If lifting things from the Earth becomes super cheap (and it most certainly can), then the vast majority of the business case for space mining goes away, and you're left mostly with mining platinum group metals for Earth use (which isn't a very big market). The narrative needs to be rewritten to account for reusable space launch.