I think the evidence should come in, for various reasons. However, there is a counterargument that it's not relevant relative to the attack, and the issue is about the attack, not about a burglary. Nelson is a reasonably skilled "spinner" of her own right, and is capable of misreading law to suit the outcome she wants to obtain. I think all judges have that quality.
If Martin was the one who was on trial, then I could see the exclusion of character evidence. In a trial, the prosecution cannot introduce evidence of bad character unless the defence first introduces evidence of alleged good character. But Martin is not on trial. What the court needs to determine is if Zimmerman is telling the truth. Was Martin a bad ass who had no lawful purpose being in that neighbourhood or an innocent person just strolling along minding his own business? Was he an angel or someone who had previously engaged in unlawful behaviour? This evidence would help bolster the authenticity of Zimmerman’s recollection. It should be introduced and the refusal of the judge to permit it could result in any conviction being overturned on appeal.
which explains why Dershowitz is recommending that the defense move to have the NEN call barred.