Reported speech
Hello Gurus of English. I have a question to ask. I have been told that I must shift tenses back when I use reported speech and I am used to dealing with it, but there is a different opinion that in some cases I don't need to shift tenses back. Do I have to follow my strategy or I need to be told about an exception?
With all my respectMy question is about the point when we use reported verbs like to claim, to threaten, to imply, to confess ets. Do we have to shift tenses back in this particular case?

Question

Reported speech
Hello Gurus of English. I have a question to ask. I have been told that I must shift tenses back when I use reported speech and I am used to dealing with it, but there is a different opinion that in some cases I don't need to shift tenses back. Do I have to follow my strategy or I need to be told about an exception? 
With all my respectMy question is about the point when we use reported verbs like to claim, to threaten, to imply, to confess ets. Do we have to shift tenses back in this particular case?

Answer

There are very rare cases such as "permanent facts", eg. She told us that the sun rises every morning.

However, almost all of the time we back-shift tenses. I've heard of the "don't shift tenses if it's still true" idea, but I just see that thinking lead to non-native phrases.

For example, it's natural to shift the tenses in sentences like these:

"What did you say your name was?"
"Henry! Your wife told me you were here!"

Honestly, I'd just listen and copy what you hear... no need to over-analyse the grammar.