In Texas, Is a Rear-End Accident Automatically the Fault of the Driver Who Hit the Other?

Automatically? No, it's not automatically the fault of the person who rear-ended the other. However, I'd say about 90 percent of rear-end car wreck cases we handle were the fault of the rear driver. 

Unfortunately, since it's not automatically the rear-ender's fault, you'll need to prove that the person who hit you caused the accident before you can make a claim against them. 

Furthermore, sometimes the front car is truly to blame for an accident. I've written a helpful article that dives deeper into these issues with examples - you can find that here:

Rear Ended in Texas? Here's What You Need to Know About Fault in a Texas Rear-End Accident