Mother's diet can help determine sex of child

That's a much better hypothesis, in my opinion.

Exactly. Correlation does not imply causation.

Whenever I hear about various things that supposedly make children smarter, like listening to Mozart as a baby, playing a musical instrument, or having a fish as a pet, I can't help but think in almost every case it has much more to do with the type of environment the child is raised in.

There was a good "Bullshit!" episode (Penn and Teller) about exactly that.

Two more theories consistent with the data are:

(1) neither affects either; (2) eating more calories creates more girls

No. 2 might seem weird but consider the fact that using the brake pedal creates fewer car accidents despite the strong positive correlation of braking with accidents.

Without testing between competing explanations, there is no science, only depleted research funds :-(

This study refers only to the moment of conception.

Of course, it might also be the case that between the 9 day trip from the Fallopian tubes to the uterus the mother's diet affects the fertility conditions of her uterus differently for XY and XX offspring (for example, making it 50% likely for an XX to implant itself but only 45% for an XY to implant).

It's not that simple. It is well-known from other research studies, particularly the ones which document the effect of social status on gender ratio, that the woman does have an ability to influence the gender ratio of her children. The most likely mechanism by which she does this is altering the porosity of her cervical channels, which could change the ratio of male to female sperm, but as far as I know no one has observed this directly.

The article poses a possible explanation at the end. The development of a fertilized embryo depends completely on the mother. Perhaps certain conditions reduce the viability of male embryos or increase the viability of female embryos. That seems like a simpler explanation than some sort of sperm selection.