Both Hillary and Romney are defending their point with half-truths.
In Hillary's case, it's a lack of distinction between different kinds of lobbyists -- she's right that, for instance, a union represents its union members, but the real problem with lobbyists is that they tend to represent only some real Americans, typically disproportionally, and typically in proportion to the power of their members. Thus, Americans for the Arts is not influential because artists are not influential, but the Oil lobby is powerful because oil companies are powerful.
In Romney's case, the thought that money that goes to corporations eventually go to individuals is also a half-truth: the point is that it goes to individuals typically disproportionally; a small number of key investors and executives, many of whom are already wealthy and don't really need government help.
Now, if we lived in a society where it was really hard for business-owners to get heard (and there are countries like that) or where people didn't have the ability to band together and lobby their congresspeople (and there are countries like that), those points would be valid. But we are currently in a society where those types of organizations have too much voice, and therefore protesting on their behalf is at best tone-deaf and at worst displays an addiction to the forms of corruption that our current system breeds.