Hello Valera,
According to your screenshot, what you mean is when first page is loaded, the site wide is already selected and same goes to the group hence the post is improperly saved, right? If so, I've fixed it for you. Now, if you didn't select the 'Site wide', it will get the group selected and the radio button for site wide is inactive. Please have a look. If this is not like what you want, please elaborate more on it.
Hope this helps.