I don't see why this would be such and important question. If we want to have faith, we only need to have faith in the Buddha's enlightenment. Whatever claims, direct or indirect, true or false, of any stream entry shouldn't be too much of a concern, as I see it. But to answer it anyway, in my understanding:
In a way you already gave the answer when you quoted "the dustless Dhamma eye". It means seeing reality without dust in the eyes, seeing the Dhamma in everything. A being that entered the stream sees this not on an intellectual level, but on deeper level. They see the four noble truths. And since these truths include all of the Dhamma, two beings entered the stream will agree on all things Dhamma, also dependent origination. They understand it as a result of directly seeing nibbana, not trough some analysis. So understanding of impermanence will be identical also.
Because the understanding is on a deep level, two may seem to disagree on a superficial level once it is conceptualized through words. Even in the suttas one can find seemingly opposing things, but that is also because they are on a conceptualized level - the level of communication.