I cannot access an index.html at http://rajshri.org/index.html however http://rajshri.org/index.php returns your holding page. This is not how I would expect the setup you have described to behave. Can you try to get a better answer from your hosting company about why they say this is not possible. I have use an index.html alongside an index.php many times when setting up a new site without problems. Perhaps they know of a specific restriction they put in place. I do not believe it is a linux restriction.
It is particularly strange that the index.html cannot be accessed via its own filename.