There's no way the Alamo is the oldest building in Texas. A cursory googlin' turns up this, for example":
https://en.wikipedia.org/wiki/Mission_San_Juan_Capistrano_(T...
https://en.wikipedia.org/wiki/Mission_San_Juan_Capistrano_(T...
https://en.wikipedia.org/wiki/Mission_San_Francisco_de_la_Es...