It seems that when it comes to indirect speech in Spanish, back-shifting of tenses occurs, just like in English (I am going...= He said he was going...). Below is a link with grammar rules for Spanish indirect speech, for reference. https://www.lawlessspanish.com/grammar/indirect-speech/
BUT in English it is also possible to start indirect speech construction with present tense and it would not employ back-shifting (in case on present or future events). Example below:
I LIVE in London = She SAYS she LIVES in London.
For events that happened in the past, I believe this would not work because it is logical to put all verbs in the past: I bought a car. = She said that she bought a car (NOT "She says that she bought a car)
Also, sometimes English native speakers go against rules in order to express idea better and be understood. Examples below:
Sun RISES in the East = My teacher TOLD me that Sun RISES in the East. [for common-sense things]
Bus LEAVES 10 minutes earlier today = Jay TOLD me that bus LEAVES 10 minutes earlier today. [to avoid confusion that bus already left that would be in case "bus LEFT 10 minutes earlier today].
Is it possible in Spanish everyday usage to break the rules in same manner, in similar circumstances? I have found one link which potentially shows it is possible. Below is an example example with a link:
La mujer de Raúl Martins dice que vive en una torre de lujo en Cancún pero trabaja como empleada.
So I got the feeling now that it can work, but only for present tense (like in English).
Please correct me if I am wrong. And will appreciate your answers.