That's was said in their own games and the official materials. So yes, it's 100% official.
Shirou can't trace Ea because "the material components of the sword have no origin on the mortal plane. Ea is the original scripture of the country of death, the root of all memory of life. As Gilgamesh puts it, it defines Truth. It is the state even before the creation of Heaven and Earth, when the planet didn't bear the existence of life - that is, Hell. Although it is not present in the records passed down, it is said to be carved down in the genes that can't be seen with the naked eye. Somehow, it is what defines that truth, what builds that Hell."
Shiki can't kill things outside Gaian system because he's part of that system. That's how Nasuverse works after all. "He sees the lifespan of the substance. It's not so much the existence or the record. It's the predetermined life span, as in what binds the object to the relevant plane of existence, in other words, the time limit, is seen. And as said in the game, lines cannot be seen on those things that can't be killed (broken) in the present era. The base power of a human user of these eyes work in relation to the limits of the humans of that era. And obviously, as an extension of that, the base power an Earthling user, be it person or object, of these eyes is going to work in relation to how the system of Earth works. Be it rock, stone, salamander, or concept, as long as it was born in this world, there's going to be something fundamentally similar with hairy apes."
That's what we know.
misekake no jibun ha sotto sutete tada ari no mama de -
Throw away the "fake me" quietly and just be myself.