I would assume that to be true as well. As someone who had only one parent available, this is an annoyingly trite opinion. Of course socioeconomic effects contribute as well, this is again trivial.
I understand the claim but I don't agree with it. I specifically don't believe the differences disappear if you correct for socioeconomic factors, however you would seriously accomplish that.
Money isn't the only stress factor, it is that a child suddenly can become the primary relation to their parent and they might even be alone with that in case of only child. Of course additional family and siblings and a bunch of other environmental factors would have an effect too.
I do think it has an influence, but it cannot be reduced to that. To state the opposite is probably just bad science like in so many cases. It is the hypothyroidism explanation of social sciences.
But that was your claim:
> this disadvantage disappears once you normalize for the socioeconomic conditions
And the tirade about families changing hints as the usual ideological slant. But for nobody under 50 divorces are anything new.