It's curious that you can probably tell the alarmist researchers by their use of the Medieval Climate “Anomaly” tag.
So when does a climate variation become an “anomaly”? Presumably only when it warms. The Little Ice Age is nowhere called an “anomaly”.
The Holocene Climate Optimum (very approx. ten to seven or six thousand years before present) when it was much warmer than at present for about 3,000 years or more, isn't called an “anomaly (and one particular member of the Climategate mafia has been very active in trying to rid the record of this prolonged warm period) . The Bronze Age warm period (it's also often called the Minoan warm period) isn't called an “anomaly” either. Neither is the so-called Roman Warm Period.
As you noted, it's very important to dis-establish the Medieval Warm Period, probably because it's the one that's best known of in a general sense.
Also, the MWP, occurring between AD 900-ish and 1250-ish, is only within about the last 1,000 years and a bit. Focussing on that keeps many people's attention off earlier warm periods, ESPECIALLY keeps it off the very long and warm Holocene Climate Optimum, which is called “Optimum” for good reasons.