Applebaum was an expert witness called in to testify on how a computer could be remote controlled, and the prosecutor tried to have him dismissed based on the retweet. He ended up testifying, so I guess the attempt wasn't successful.
I don't think that's a technically ignorant argument for a prosecutor to make. There's certainly a factual inference that could (but does not necessarily have to be drawn) between retweeting and being friends. Especially in the context of getting someone disqualified based on conflict of interest.
There are many people I retweet whom I have no connection to whatsoever. I like what they wrote and I think it's relevant to or interesting for my followers.
Generally, information that has absolutely no merit in a court case isn't allowed in the courtroom because (I presume) it can subconsciously alter a person's judgement of the proceedings.
Assuming a retweet is the full extent of their "friendship", this is the real-world equivalent of dismissing an expert witness because the defendant quoted them in a paper once.
Something like a tweet is context dependent. Some people tweet mostly to their friends and a lot of retweets are in fact indicative of a personal relationship. It will often be easy to estimate for a twitter user, but very hard to make objective enough to work as evidence in court.
Do they have just 12 or 12000 followers? Are they tweeting personal tidbits or politics & jokes? etc. These things can add up to an very informed guess.
In the U.S. The admissibility of evidence is based on relevance.[1] The modern formulation asks: does consideration of a piece of evidence increase or decrease the probability of some material fact being true?
A retweet is certainly relevant. The evidence makes it more likely that two people are friends than the baseline where there is no retweet.
I understand the ignorance displayed by the judge here, but did the judge also see being Applebaum's friend as a bad thing?