MJ's primary argument is basically that the absolute article count for "autism vaccines" has grown. The count for "autism" has simply grown more. I say that the relative count is what matters, but let's look into this in more detail.
As I've noted in comments, MJ fails to take into account that the total number of articles indexed by Google News Archive has also grown from year to year. Presumably, this doesn't mean people are reading more newspapers, but simply that Google is adding sources to its index all the time.
Estimating the total number of articles in Google News Archive could presumably be problematic algorithmically for Google. I have some ideas which I mentioned in comments, but I'm not confident that they would be unbiased.
Instead, let's check if searches for "autism genetic" relative to "autism" have the issue MJ thinks relative counts have.
They do not. There's no peak in 2002 here. There's no downward trend after 2002. There's no dilution of the word "genetic" in autism articles as more topics are covered. What we see instead is a remarkably stable trend.
We previously also looked at relative counts for "neurodiversity", which MJ had verified as well. This analysis also fails to support MJ's hypothesis. The same is the case of several other trends I've checked which I'm not going to go into here.
It's also illustrative to look at the raw article counts for "vaccine injury" (in quotes). These counts are presumably also biased by increasing coverage of autism topics, but maybe less so.
What we see here is consistent with a peak in 2002-2005, and a brief recovery in 2008 due to substantial propaganda efforts in relation to Jenny McCarthy and Hannah Poling. This effect cannot be expected to last very long, though.
MJ has failed to explain why the pattern of media coverage for "autism vaccines" generally matches VAERS autism submission trends and the number of autism cases filed with the vaccine court. It's lazy and convenient to simply say "the data was not meant to track this." What is the explanation?
Additionally, Smith et al. (2007) reports that:
MMR vaccine remains the number one ‘top of mind’ vaccination issue for parents. The proportion of parents believing MMR to be a greater risk than the diseases it protects against has fallen from 24% in 2002 to 14% in 2006. The proportion of ‘hard-core rejectors’ of MMR vaccine remains stable at 6%. There has been a gradual and sustained increase in the proportion of parents across all social groups saying MMR was completely safe/slight risk rising from 60% in 2002 to a current level of 74%. There now appears to be a sustained move away from fears over MMR safety and belief in the unfounded link to autism towards a more positive perception of the vaccine.
Finally, an immunization report by the British NHS shows that MMR coverage had a low in the 2003-2004 period.
I've perseverated on this a lot more than I probably should, and I've gone out of my way to address ridiculous criticisms put forth by MJ.