I'm not trying to get an infraction here.. but this sounds more like a personal issue that you have with Hostgator OP. Otherwise, why would you be targeting them?
Firstly, correct me if I'm mistaken, but I believe EIG actually kept the same data center and support staff for Hostgator when it was bought.
The big hatred for EIG actually comes from their migrations. I actually used to work for EIG, and all day nearly all my customers were calling in for legitimate help with somehing, and they would constantly be praising the hosting service. Then there's the few odd calls where so called "programmers" mess up all their code and think there's something wrong with the servers.. until I prove them otherwise. Or have their Wordpress site hacked, and think it is the Web Hosts fault, yet they haven't logged in to update it in over a year, nor took any other precautions to protect it.
But the real hatred for EIG from people is coming from the migrations. Like jeez, I was there for some where they had 600,000 accounts to move. Not to mention some of those accounts can have like 100 email accounts. It's not easy to do, but it's understandable for people to get angry at them. Scripts are used to mass update everything website and connection strings, etc. It doesn't always work out that well for everyone.
But anyways, I would get customers who call during a migration, and they would be so angry and cancel their services. Then they would call right back to another EIG property and get me and signup a new account. And I'd speak to them a few times over a 3 month period and they would be like "OMG you guys are such an awesome company! Way better than that last company. Their support sucks! Their servers suck! They just suck!".
The funny thing too is, a lot of those people would ignore migration emails which would give them great suggestions in regards to making sure the migration went smoothly. Like telling them they need to update their A record since we didn't control their DNS. Or to check their site on the new platform (temp url) to make sure everything is working for migration(and contact us if not).
But yeah, aside from the migrations, they're not that bad of a company. That's the only difference between them and other shared hosting companies. Is that they have a monopoly of web hosts and frustrating migrations. What are companies out there own that many though?