Random looking balls of data points don't have slopes. It is invalid to perform a linear fit on data that does not derive in large part from a linear generative process. And presenting a fit from a model that is facially absurd to apply is bad data science. Whether or not an informed reader would discount the absurd model fit is not material to whether it is appropriate to present such a fit.
They could have binned the data and plotted percentile bands. They could have used a non-parametric density estimator. There are lots of things they could have done to summarize the data and make some sense of the ball of points. But linear regression with slope error bars is not an appropriate choice. That it is easy to compute linear fits, and that it helped them make their point is not justification.