I don't believe that's correct. Solar flares are associated with sunspots, and sunspot size correlates to the size and strength of the associated magnetic fields and therefore potential flare strength. Large sunspots are just as likely (as far as size distribution) when the sun is highly active, and there tend to be more of them.
Here's an image from May 1, 2003, during the peak of Cycle 23, a fairly active cycle. Note the very large sunspot near the middle of the solar disc. It's many times Earth-size.
You can read the archived spaceweather.com page here. It discusses the flare potential for those spots.
I found this interesting paper on solar storms. It contains a table of "great solar storms", and while the 1859 event was during a low cycle, many of the others were during very active cycles.
What is true is that low cycles like 24 and (most likely) 25 can still produce large sunspots, and severe solar weather.
For those interested in comparing the current solar cycle with historical data, I recommend keeping an eye on the Layman's Sunspot Count. Despite the name, it's a very professional attempt to compare current solar activity with activity during the Maunder and Dalton minima - something the "official" counts are doing poorly.