The problem is the 'pop sci' reporting. "Earth-like" or "second earth" could easily be swapped for "Venus-like" or "second venus" in 99% of cases where pop-sci uses "Earth like" and still be factually correct.

However, Wobbles and Transit photometry are done over time and plot trends which definitively show that something with a certain mass is orbiting with a certain period around the star. There isn't really anything else it could be except an exoplanet, unless our understanding of how physics works was way off, which we know it isn't.

as for Spectrography brabel sums it up in their comment very well.