How have changes in communications technology affected the way that misinformation spreads through a population and persists? To what extent do differences in the architecture of social networks affect the spread of misinformation, relative to the rates and rules by which individuals transmit or eliminate different pieces of information (cultural traits)? Here, we use analytical models and individual-based simulations to study how a 'cultural load' of misinformation can be maintained in a population under a balance between social transmission and selective elimination of cultural traits with low intrinsic value. While considerable research has explored how network architecture affects percolation processes, we find that the relative rates at which individuals transmit or eliminate traits can have much more profound impacts on the cultural load than differences in network architecture. In particular, the cultural load is insensitive to correlations between an individual's network degree and rate of elimination when these quantities vary among individuals. Taken together, these results suggest that changes in communications technology may have influenced cultural evolution more strongly through changes in the amount of information flow, rather than the details of who is connected to whom.