You say '(I) assumed that the letters assigned to Indian sounds in English are always consistent. That's not a good assumption'
It is a necessary assumption for any transcription-system to work.
All users need to agree from the start what each English letter (-combination) stands for. The system Lala
used, 'Self-Pronouncing', is called self-pronouncing because every letter is pronounced in the most obvious English manner. By using 'th' for a dental plosive, Lala
broke that rule. (And by using the same 'th' for 2 different sounds, 'd' and 't' she broke another).