The way this sort of research works is by modeling weather under different conditions and determining that certain weather patterns are statistically more likely under conditions consistent with global warming. This isn't just "it is hot for a week so that must be global warming". It is "the air patterns that are required for this sort of thing to happen are highly associated with higher average global temperatures". The causality is going in the other direction.
But the BBC article... "the research has not yet been peer-reviewed.
"They used 21 climate models to estimate..."
"They compared the climate as it is today, with the world as it would be without human-induced warming."
This is not empirical science. And by using a 1000 year model they are starting their analysis, conveniently, after the peak of the Roman Warm Period.
They don't seem to be using a 1000 year model, they are just saying the rate of occurrence. And when do you think the Romans, and their related warming period, were exactly?
Edit: oops I did mixup the late Roman and Medieval warm periods. Anyway both the RWP around 2000 years ago and the MWP 1000 years ago are what geologists call interglacial periods. The earth is currently in an ice age (when there is permanent ice at either of the poles) but every thousand years or so the climate warms and the ice retreats for a couple hundred years. Unfortunately most climate change studies only consider data from 1850 onwards, and those that do go back further only go start at the last glacial period about a thousand years ago.
Edit to match your edit: Neither the MWP nor the RWP were global phenomenas - they were hotspots at different times for different regions. What we are currently experiencing is a GLOBAL increase.
Also worth noting this from your article... "During the following Little Ice Age, which lasted roughly from 1300 to 1850"
There's that 1850 again, the climactic minimum, and coincidentally the exact year that climate change models start from.
"1550 to 1850 AD Little Ice Age Coldest temperatures since the beginning of the Holocene. Populations die from crop failure and famine in Europe." http://www.atmo.arizona.edu/students/courselinks/fall12/atmo...
An old friend of mine is a professor who studies climate change. They fairly consistently get hate mail from people who insist that computer modeling as an entire discipline is utterly worthless and should be dismissed without any investigation. There are no reasoned criticisms coming from the denier community.