I don't believe the river analogy actually _requires_ multi-universes, it requires, rather, an ability to speculate and ask 'what if?' questions. These _may_ unearth ideas, hopefully some testable, that show us otherwise hidden structures and configurations. The 'true explanation' regarding geology and river pattern is 'plain' to those of us who have seen other evidence (of strata, rock hardness, topography, other river systems): how might the geographer have come to a clearer view if he was, say, on a planet with one giant continent and one massive river system? By looking at the pattern of the river, he probably wouldn't get the necessary insight - by looking at its dynamic change over time, it's underlying rocks, the interaction over time with that geology, etc, he may have. Assuming a tuner, something tunable, something tuned, etc, explains nothing and is akin to the geographer saying the same of his singular and single time=frozen snapshot of a river system. It gets us no further, we dead-end on the 'unexplained explanation'.
Nor does it 'ignore' fine tuning: my point is that 'fine tuning' conceptually requires something special to tune to / to tune it. Looking backwards, we posit that that something special is us: we exist: the universe appears to be run according to constants, limits and algorithms that would only need to be slightly off for us to _not_ exist... and conclude that _therefore_ it is fine tuned especially for us. Now, clearly, this anthropological argument makes a certain psychological sense: we each of us, anyway, have only our very own perspective - psychologically, it makes a certain sense to go further and contend that the universe is fine-tuned especially for 'me' (which is part of why death and finitude give us such existential shocks when first we meet them, and realise they apply to us also).
However, I think it a hubristic and unproven form of argument. Sure, we would not be here otherwise. But, is there any other than a psychological reason (of comfort) that is a strong enough reason to 'prove' (as opposed to be a piece of potential evidence toward a proof) the contention that, rather than 'we are here because of the values for the constants, limits and algorithms that define our space', 'we are here because the values for the constants, limits and algorithms that define our space are chosen, designed, tuned specifically in order _to_ lead to us / me'?
This is not to dispute a logical possibility that the 'tuning' is not only that (tuning), and to a theme (us), but is also enacted / caused with the _purpose_ of leading to 'us' by a 'tuner' (creator; god; intelligent space monkey, Cthulhu...). But, I see no _proof_ of the contention, nor sufficient weight to the purported evidence to convince me that it is so.
Conversely, that it is not so also has a proof gap, and given the lack of outside-the-rules action in the world no chance of filling it.
My position of not only skeptically doubting the design/fine-tuning/anthropological argument is only tipped, for myself, over to a slightly firmer conviction that the fine-tuning argument is fallacious by application of Occam's razor with a side order of Popper:
Karl Popper argues that [...] Our preference for simplicity may be justified by its falsifiability criterion: We prefer simpler theories to more complex ones "because their empirical content is greater; and because they are better testable" (Popper 1992). The idea here is that a simple theory applies to more cases than a more complex one, and is thus more easily falsifiable. This is again comparing a simple theory to a more complex theory where both explain the data equally well.
(en.wikipedia.org/wiki/Occam%27s_razor#K ... arl_Popper
I see the razor as a tool or rule, not a law, but nevertheless one to be taken seriously. Thus, if two competing theories each have a very different series of questions begged by them, applying parsimony makes sense, and then to successfully argue for the _less_ parsimonious will only be viable when good reason can be given to expect _more_ implications, factors, background assumption or whatever rather than less.
Applied to fine-tuning, both the argument that 'the universe is fine-tuned' (and one of the corollary goals of that fine-tuning may be our very existence) and the argument that 'it is not a case of "fine-tuning", but, rather, just a coincidence whose "staggering" nature is not objective but merely a projection of human hubris', are question begging.
The latter uses empirical data and scientific proof as limited to direct and indirect mathematical requirements and physical measurements etc, which it is generally agreed 'cannot speak' to the 'outside' of their picture (assuming instead a gap they may one day fill, as more coherent than expecting said gap to be filled already by the already increasingly absent seeming and rather non-specific and material-property-less catch-all of a 'god' or other super-natural idea).
The former requires, at minimum, unproven and possibly unprovable teleology / purposiveness, plus the entity science cannot interact with as mentioned in parentheses above - an entity that somehow acts on the physical world, or did at some initial point at least do so, but upon which the physical world cannot act; that purportedly 'prayer' or 'meditation' may be able to influence, leaving the goal-posts moved to (again) a part of each of [physical and thinking beings] that somehow acts as a bridge between a physical world and the special other reality implied by the need for a 'tuner'. The unsatisfactory nature of this kind of rule-free dualism has meant that I have never been either comfortable nor convinced of the possibility. The logically 'cleaner' 'solution' of co-incidentalist dualism, wherein no interaction takes place between two posited realms of which only one can we 'know', 'explains' nothing, and, unlike science (which has areas it cannot yet explain, but it at least holds open the possibility of future knowledge [not through death or rapture]) does not seek to 'explain' - it is, in fact, surely, the end of thought and the death of reason.
So, no neat tidy answers we can cleave to as proven fact, this is still firmly in the realm of us philosophers on several counts, but for myself I definitely fall on the side of the debate that treats 'fine-tuning' as a fallacy. As a rationalist with materialist tendencies, I can, like Dawkins, safely say I would alter my view if appropriate new evidence / argument appeared - but, also like Dawkins, I think this nominally open-handed and magnanimous gesture to be a safe bet on my part, and thus potentially disingenuous! Nevertheless...