Well, according to some data I found[1], GoDaddy has 36 million registrations, while the next closest registrar is Enom at 9.7 million. In fact, GoDaddy has more registrations than the next six most popular companies combined. So, it probably makes sense that most of the registration-relation things you hear about involve GoDaddy.
To be clear, these are instances of domains specifically being moved to GoDaddy.
When I have spot-checked lists of seized domains in other cases, domains registered with GoDaddy were serving the ICE seizure page while domains with other registrars were simply down.
