Hi, this has been reported and discussed before. While it may not seem intuitive, this is the expected result in Corona. Those shadows are caused by material reflectivity. They will disappear if you set IOR to 1.0 for your materials - they will not be reflective any more, but at the same time they will not be realistic. Those shadows are a part of reflection.
If you need to get a reflection override of some bitmap without seeing the "additional" shadows, you can try clamping the HDRI to remove the brightest part from it (aka the sun). See screenshots.
It is also possible that the result you are after can be achieved using some other way. Can you explain why exactly you would like to use the reflections override? We may be able to provide some additional solution or workaround.
