We probe structural and discourse aspects of coreferential relationships in a fine-tuned Dutch BERT event coreference model. Previous research has suggested that no such knowledge is encoded in BERT-based models and the classification of coreferential relationships ultimately rests on outward lexical similarity. While we show that BERT can encode a (very) limited number of these discourse aspects (thus disproving assumptions in earlier research), we also note that knowledge of many structural features of coreferential relationships is absent from the encodings generated by the fine-tuned BERT model.