I don't think it's there to mislead someone on purpose, I just think people feel uncomfortable pointing out Texas is killing people that are innocent and thus end up not pointing it out or accidentally making things sound like "oh no, Texas is going to make a mistake they don't normally make!"

It is clear that it is meant the shaken baby syndrome is what is the first here, but still it could be taken the other way, and it ends up downplaying how contemptible the State's actions are, even though the poster really wants to highlight that.

I guess I would prefer something like -

"Texas, continuing its tradition of executing innocent people, will for the first time use the dubious science of Shaken Baby Syndrome as its cause."

It's not just the post, everybody does it whenever they say "Texas might execute an innocent person" they ignore that Texas has executed people that were extremely likely to be innocent (so likely that it is reasonable just to describe them that way - in case anyone has problems with my phrasing here)