Can you outrun a tornado in your car? Short answer: Yes; but, it's complicated.
When it comes to taking shelter from tornadoes there are several factors that come into play. Time of day, your location, who you're with etc.
When a tornado warning is issued, research has shown that you typically have 13-minutes or less before the the tornado hits. If you're going to use a public shelter, make sure it's somewhere close to where you live. In 2011, a family was caught outside of the Tushka, OK public shelter and survived the tornado by holding onto a parking rail during an EF3 tornado.
Vehicle fatalities account for 10-20% of tornado fatalities. Many of these are from trees falling onto cars. Cars are built for impact and can often provide somewhat safer shelter than mobile homes which accounted for 68% of tornado fatalities in 2019.
The smallest little room of a permanent structure can often provide you with the best protection from flying debris. The exterior and interior walls will slow or stop airborne debris.