If you use your debugger, you'll see that Windows will set the Capture property to 'true' before the Control's OnMouseDown is called and set it to 'false' after the OnMouseUp. So, the default behavior is to capture the cursor when dragging on a Control. This allows auto-scroll behavior to be implemented without having to set Capture at all. You have to go out of your way to not capture the mouse.
The other factoid that I'd like to share is that if you have a bug where your mouse click events are being caught/eaten/trapped/absorbed across the whole screen, then there's probably an errant call to Control.Capture = true. For example, in our code base, someone was calling Capture = true in a Control's constructor, thinking that the Capture property was a persistent permanent property and this led to the bug where the first mouse click anywhere on the screen was being sent to this buggy Control. The second and subsequent mouse click events were routed as expected.