evidence can be, and should be, presented at lower level court even if the lower court doesn't "allow" it. as long as the evidence is part of "the court record" the evidence can be raised upon appeals, including specific appeals as to the lower court's ruling that said evidence was deemed inadmissible.

for example if a defendant accused of murder had a video tape of another person killing the victim and that lower court ruled the tape was inadmissible for whatever reason, a higher court could exonerate the defendant by finding the lower court erred in their ruling on the inadmissibility of the tape