Yes. But even worse, adding data can actually make the situation worse by making the erroneous topology well-supported, and deluding you into thinking that the 'fake' clade is 'real'. The tree looks 'better' (nicer bootstrap or posterior probabities) but the topology is 'worse', because homoplasy is no longer the 'noise' but the signal.
There's also the matter that improved taxon sampling. Some lineages make life difficult by leaving us only a few lingering species.
That counts as bad luck.
No, the "wrong model" isn't the problem here; they tried many different models (four substitution, four among-site rate-heterogeneity), which are used today.
That makes 16... Modeltest tests for 56 models...