Optional tense back shifting [duplicate]

When they said relevant I think it meant still active in that moment. For instance:

Mary: I've lost my keys!
John: What did she just say?
Lucy: She said she has lost her keys.

But, if the John asked Lucy a few hours after Mary's sentence:

What did she say when we were at the shop, I didn't hear it well?

Lucy would say:

She said she had lost her keys.

If the time difference between the earthquake and the president's acknowledgement of such disaster wasn't very long, then it is optional. If we are talking about time span of, let's say, one day, it will be back-shifted because it happened yesterday no matter the consequences of his knowing now. We don't say Tesla has invented the light even though we feel the results now. Therefore it's optional when the time difference between actual action and the results/consequences is small. Also, you cannot think of actual consequences of the action itself and the consequences which is meant by sentence. Consequence in the sentence means it is still in progress, for example She has lived there for five years (and she still lives there). The earthquake happened at that moment, and that's it. A few hours after that, it belongs to the past. But you can say there have been 500 injured people from the earthquake so far (there have been since the earthquake happened and maybe some more injured people would be found). As for your question about introductory verbs in indirect speech, they don't distinguish whether back-shift is optional or not. There are some which require subjunctive, but apart from that, they all require back-shift unless the aforementioned context interferes.