Here's a thought: why are we pressuring legislators when they're mostly accountable to their donors and party bosses? Why don't these sites track those people instead?
They are ultimately accountable to the public, to an overwhelming degree. When the public does not care, that allows the other influences, which are ultimately much smaller to have an outsized influence.
By not being consistent in caring about the outcomes of votes, the public has allowed other groups to not only have an influence, but to have it often. That trains representatives to consider those other groups on all votes, as those other groups are much better about keeping track of what the representatives do and holding them accountable later.
So in the end, a small and weak but consistent group ends up having a disproportionate amount of influence compared to a large and powerful but largely inconsistent and absent group.
What this means is that it both is, and is not a myth. It's true that donors and party bosses have a lot of power, but it's also true that the constituents control all the power, and it's only their lack of involvement that allows those donors and party bosses to have the power they do. Were constituents to become much more interested in everything their representative did starting tomorrow, the power of those donors and party bosses would vanish fairly quickly (depending on how likely the representative considered the increased interest to continue).
Also, the paper doesn't ascribe any reason for the effect. All that stuff about campaign finance is just editorializing from that video. It's just as possible that, for example, wealth and education are well correlated and Congress is siding with the well-educated 6% of the time.
The truth is congress does what donors/etc ask when people don't ask them otherwise.
So it only happens on a small set of issues where people don't seem to care.
Additionally, the mechanism that causes this is not actually the money. It's nice to think that, but it's really: They don't understand the issue, they mostly trust the lobbyists they know to tell them what the good thing to be doing is. IE the lobbyists are long time friends.