I have heard this opinion echoed by Indians, the combination of both the outside not being their problem, and thinking someone else (lower caste) will take care of it.
There are city workers and occasionally homeless people who pickup trash (to salvage or sell). I'm not sure how this opinion of theirs is formed but I can assure you nobody is throwing around trash with anything remotely caste related in their mind. It isn't even in consideration.
Its plain old apathy and no sense of responsibility or shared ownership. Outside is just something you share with other 1.4 billion people of the country.
The cycle usually goes like one idiot starts throwing trash, other idiots start adding their trash too, few weeks/months govt workers do a bare minimum job of clean-up, repeat.