Can an HDRI light "pass through" an object?

I have a backdrop /stage set that I use quiet often which is like a giant fish bowl. I place the object/s I want to render at the center base of the fish bowl, light and render.
If I want to use HDRI though, it always picks up the giant fish bowl and darkens the view of the main objects.
So my question is can you have a object that is visible to the camera and standard area lights, but the HDRI casts light through it ( doesn’t see it)?
If so, how would I achieve this?

Many Thanks

My story… I was curious about that too, so I put the camera, a small cube and a shiny silver ball inside a BIG cube. The HDRI was a very bright, empty warehouse. No other lights. Eevee.

The shiny ball reflected the HDRI (but not the small cube), and the small cube appeared to be lit. I was surprised.