The relationship between downsampling and frequency resolution
Your understanding is correct. I don't have the full text of the paper, but it sounds like they aren't being very precise with their description. As you pointed out, downsampling doesn't improve frequency resolution in and of itself, it merely reduces the amount of bandwidth that can be represented unambiguously.

However, I can take a guess at what they were referring to. Assuming they are using a DFT for spectral analysis (the common choice), note that the fact that for a given DFT size $N$, the output bin spacing is a function of the sample rate:

$$
f_{res} = \frac{f_s}{N}
$$

So, if a smaller frequency resolution in your spectral calculation is desired, decreasing the sample rate of the data can help you do that. Of course, you could also increase the DFT size $N$ as well; there are some applications where that's not an option, though (e.g. if you're using hardware that is limited to certain FFT sizes). Also, this method can have advantages when the signal of interest is in a small band of frequencies relative to the original sample rate; in this case, downsampling followed by a smaller DFT can be more computationally advantageous than doing one large DFT (this is known as the zoom FFT technique).

Note that there isn't a free lunch here: to actually realize an increase in resolution, you need $N$ samples at the lower sample rate, which requires a longer observation time. This is the same total observation time that is required by just collecting more data at the higher sample rate and then doing a larger DFT.