Bhagavad Gita, Chapter 17, Verse 15

Speech which causes no vexation, and is true, as also agreeable and beneficial, and regular study of the Vedas, these are said to form the austerity of speech.

Real discipline of speech is defined here by more than just avoiding lies, it also has to avoid real harm.

Truthful words still have to be inoffensive and beneficial to actually count as this kind of austerity. Real care in how something is said matters as much as whether it's true.