All the quotes you have quoted so far does NOT prove preferential treatment. Like I said GE uses a rather "universal" approval standard across all of its offering. If you can get one, you should have no problem getting the second one, since the second one uses a very similar standard compared to the first one. It doesn't matter where you apply from.
This is what preferential treatment looks like. AMEX uses an AMEX internal risk score which scores existing AMEX account more heavily (more percentage) than anything else.
GE's internal score treats every account (non-GE or GE account) the same. It does not give more percentage to GE account.
I've had cards for Walmart (recently CLI'ed to $2000 from $1000) and Belk (recently CLI'ed to $1000 from $200)for quite a while, both are GE backed. Last year, I moved from an apartment into a house. The person moving into my old place offered to buy the existing furniture. The house was partially furnished and I financed about $3500 from Ashley Homegoods and decided to splurge on a mattress and financed $3400 from Tempurpedic, both GE backed cards and both offered 0% financing for long periods of time. I paid both cards off within 4 months. About 3 months after that, I tried to get GE financing for a medical procedure that cost $1900 but GE would not approve because of the new credit I had gotten with them, even though they were paid. But last month, I applied for the Paypal Extras card and got instant approval for $2000.