I think that on the 1911 Census,"Institution" just means any large building that is not the family home/house.
So it could be a sinister meaning,but it could also mean a Hotel/boarding house/or the place they were employed in that provided accomodation.
After reading about it,I looked up King George V & Queen Mary,and both their entries have "Institution" listed,so I don't think Buckingham Palace could be classed as a Mental Hospital.
On second thoughts................