Need More Info On Isolation Transformers

[TinCanAlley]

Okay, I understand the basics behind using one, but in my reading I've run across something I need a bit more understanding.

I keep running into not needing one if the device has a transformer. If I'm understanding this correctly, if the device gets power from a two prong and the neutral side goes to the chassis, and the hot goes through rectifiers and such, you need one. If the device has two prongs and goes directly into a transformer to create the voltages necessary for the circuits, you don't need one. Is this correct?

I'll use my Zenith as an example. It has a transformer. If one isn't necessary, I feel better about scoping a few years back. If it did need one, then I feel lucky I scoped it without issue. Is the Zenith Avante with a transformer okay to scope without one?

Same with my Pioneer SX-1080. It has a transformer. So is this an example of a device an IT wouldn't be necessary?

I really don't have anything that doesn't have a transformer, but I understand many TVs from the 60s and earlier didn't.

Thanks for the input. I want to put my Zenith back into diagnostics for the jailbars, but now am not sure it is wise without and IT.