My experience working with a very large app is that, yea, they basically do.

Or at the very least, you get yourself in a certain relationship with Apple that it sort of is like this.

When we had a version we needed to get through quickly due to a bad bug, we'd shoot our contact an email, a few leadership members had this contact's phone number if needed. We'd make a call, and within an hour we usually had the version approved. Sometimes it did come with a caveat of "you're going to need to fix this issue before the next update" or whatever if we hadn't quite followed the rules, but they gave us a bit of leeway in emergency situations.

This does not really mean all updates went through this super fast process. We had to wait weeks at times for app approvals. So it's not really VIP reviewing, it's more like VIP treatment if you're big enough and know the right people.

Edit: and yes, we often ran into the situation of the previous version did something that we figured was fine, and approved by one reviewer but then the next update was flagged as no good by the next reviewer despite the last one approving it.

This process seems to be available to regular apps too now. When Apple rejects an update, they ask whether it's a bug fix update you need approved quickly. If yes, you can resolve the identified issues with the next update.

They started mentioning this in the past few weeks when I was updating clients' apps.

it's a little different. In our case we were circumventing requests to make changes to the app to get approval. We were effectively getting a free pass to ship the version with a possible App Store rule breakage, this one time, and getting it approved super fast.