Few quick points:
1. Capital does contribute to the production process in the form of organization and that part should be treated as remuneration for work. However, capital has also the capacity to extract payments exceeding that remuneration, due to its ownership privileges (economists call that rent). Only the latter can be considered exploitation.
2. According to Marx, exploitation occurs when the surplus generated by labor is not returned to the laborer but retained by someone else. So it does not matter whether that surplus is retained by a capitalist or "society" or rather its representative - in each case it is 'exploitation.' It can be of course argued that 'society' returns the surplus back in the form of providing public good, but so does the capitalist i.e. by funding extravagant consumption, the arts, or by plain reinvestment.
3. There is a different between labor and laborers - while "labor" in general may not be exploited i.e. by getting the entire surplus for itself (as in a cooperative), individual laborers almost invariably will not receive an equivalent of what they produced for a number of reasons, chief among them being than in any complex organization it is impossible to measure individual contributions with any precision. So the bottom line is that individual will always be "exploited" in one form or another within this framework - so this framework is quite useless to discuss individual exploitation. However, when we want to apply this framework to labor viewed collectively - the difficulty is to draw the line between what is and what is not labor (see point 1 above). However, without drawing that line, the concept of exploitation is meaningless. So the whole framework boils down to identity politics: who is in and who is not considered "labor."
These are my 3 cents.
Wojtek