Brown bears are omnivorous, eating anything that they can get their paws on. 棕熊是杂食性动物，抓到什么吃什么。

有人说这句中的现在分词短语 eating anything that they can get their paws on 是非限制性定语，这种说法对吗？这个现在分词短语是非限制性定语吗？如果真是的话，它可以离被修饰的名词 brown bears 这么远吗？