I see what you are saying but feel it needs some clarification.
When you increase the focal length from 50mm to 200m you do actually reduce the Depth of Focus, it isn't an optical illusion. However, since you have also moved backwards to keep the subject the same size in the frame the increased subject distance has increased the depth of focus. The two have exactly cancelled each other out.
The 2 images will look very different due to perspective - which is what you are getting at. The longer lens has a much narrower field of view, so effectively a smaller area of the background is stretched over entire frame compared with a shorter focal length. This makes the background much smoother, increases subject separation, and looks like the depth of focus is reduced even when it isn't (since the background looks more blurred). The opposite is true for wide angle lens compared with 50mm, a very wide area of background is compressed and squeezed into the background of the frame, creating a busier more nervous background.
This does raise a useful teaching point. Most people want a shallow Depth of Focus so that they can separate the subject from the background better. Depth of focus is 1 tool to do that, but perspective is another, often more powerful tool. You get a much better subject separation and isolation using a 200mm lens than a 50mm prime, even if the 50mm prime is over a stop faster.
This leads to a second point. People often want shallow DoF in order to generate Bokeh. However, Bokeh describes the quality of the out of focus rendering, not the actual depth of focus. A fast prime can have very bad bokeh shot wide open at f/1.4, a slower lens shot at f/5.6 can have beautiful Bokeh. Bokeh can also be improved by increasing the distance form the subject to the background, avoiding high contrast background, stopping down a little and using longer lenses.
I think this pretty much covers everything related to DoF!