How Do Leading Manufacturers Produce Their Cameras?

It's a good question and there is a range of approaches.

Let's start from least sophisticated to most.

Relabeling: A lot of big companies simply find already made Asian cameras and relabel them. They'd argue that they 'choose' the right camera but there's little innovation there. It's basically brand / support / sales. See: Beware Phony Manufacturers

Basic Design: Some big companies will 'design' cameras mostly by picking what components and bells/whistles to include. A lot of time the 'design' is simplistic and is little more than what a consumer would do at Dell.com when picking a computer.

Advanced Design: A smaller number will do advanced mechanical design for specific high end features or niche form factors. They typically still have someone else actually build/assemble.

Software / firmware: Real manufacturers typically develop their own software / firmware in how to control the camera, how to control streaming, how to access the camera, etc. If someone is truly a 'manufacturer' this is expected.

Core components: Rarely, even true big manufacturers, design/make their own imagers and encoder chips. There are exceptions - Sony, Panasonic, Axis to name a few - but generally imagers come from Micron, Omnvision, Sony and encoder chips come from TI, Ambarella, hisilicon...

As for owning their own factories, most do not, but to me, owning a factory is not critical to being a 'real' manufacturer. That said, I do wonder how much owning a factory contributes to overall price advantage.

It makes a lot of sense that outsourcing such components is more cost-efficient. Cost-efficiency probably is not the most concerning problem in the high-end market or has it been that big of a factor historically for those companies who produce their chips in-house (assuming Axis) instead. But when the customer is more price sensitive (as for small installations and emerging markets) then in-house chip production can probably make for a cost disadvantage.