There is nothing "dodgy" in what Vicky is saying (or the medivisas website). There are simply more options for those who hail from the Emerald Isle due to the way EU law works. Having a valid ROI passport doesn't unmake her a national of the ROI. In theory you would be able to apply under EEA rules.
In fact, those from the England, Scotland and Wales could exert their treaty rights outside of the UK for a period of time and then take advantage of the EEA family path as well, but there are some well defined guidelines to that as well (something like 4 or 5 years exercising your rights elsewhere in the EU, something like that, I know someone will come along and bop me on the head with the right information)