Spider is a dominant trait. This means that unless the animal in front of you is a Spider or Spider combo, it does not carry any part of the Spider gene (nor any of the quirks that come with it). For this reason, lineage is irrelevant - it's either there or its not. If lineage were relevant, there would be a way to successfully separate the Spider trait from the associated behavior. Unfortunately, this is not the case.
Could you provide more info on the claims you've seen? Are they keyboard warrior claims or are they supported? My guess is the first, but I'm eternally curious. If they are supported claims, by who and what relevant evidence/documentation do they have? Thanks!