No, we might reject them all. If we do, it will be because they have failed to meet the required standard (i.e. the evidence must be sufficiently sound that faking it would require a greater miracle than the alleged supernatural event itself would be).
It's logically impossible to present empirical evidence of supernatural phenomena to a dogmatic materialist.
Nonsense. Plenty of people (though not you, so far) have presented empirical evidence of supernatural phenomena. (For instance, I recall one instance of a stigmatic priest in the DC area a few years back.) None of the evidence to date has gotten anywhere near the threshold of being convincing (see above), but it obviously was not "logically impossible" to present it.
That standard works for me, although we probably understand it differently.
Plenty of people (though not you, so far) have presented empirical evidence of supernatural phenomena.
OK. Here is a list of ongoing miraculous phenomena available to the public for examination at any time, which have also been the subject of rigorous scientific investigation.
The Eucharistic Miracle of Lanciano
The Shroud of Turin
-Shroud linked with Sudarium
Fatima
Image on the tilma of Guadalupe
Incorrupt bodies of the saints
The blood of St. Januarius
Hmmm... I wonder which it will be?