Harry, I'm giving you a gold star! The impression I get is that few people get as far as you have in analyzing their matches. Heck - half the people who match me on AncestryDNA have only tested within the past year! Practically everybody is new at this, so the first thing you have to be aware of is that you might be "ahead of the curve".
But take it from one of the few who has analyzed the whiz out of his own AncestryDNA matches. They're definitely NOT false matches, and while an NPE is possible, it wouldn't be my best guess.
It sounds more like a couple of match groupings I have, except smaller, and more closely-related. One of these groups has over 55 matches, who all match each other in some way. The highest one is 65cM, and is a known 3C1R (actually she's related 2 ways, so also a 4C1R). Between the handful of known relations, and the fact that a bunch of them have a Heckathorn in their tree- even though they don't go back far enough to make the connection - it's pretty clear that they're related through my gt-gt-gt grandma who was a Heckathorn, and came from a huge family. A few of us are on GEDmatch, and match on a common segment.
One of the known relations is a half-6C, so if he's not also related some other way, I know EXACTLY where that segment came from - my gt-gt-gt-gt-gt grandpa Heckathorn, who came over on a boat from Alsace in 1750! That might be kind of a "big IF", but it would really just make sense.
The thing is, my segment there is about 42cM long. On the one hand, that's unusual to have from that far back. On the other hand, there are so many ancestors that far back, that you're likely to have some of these! They call these "sticky segments" - segments that have managed to "stick together", not being chopped down by recombination, over many generations.
I have another group that's just as big, and all I can figure is that they must connect up within the unknown ancestry of my gt-gt-gt grandpa Standley. I've found people in those matches who are VERY distant cousins to each other, going back the a couple in the late 1700s. The surnames involved existed in the same place as my Standleys lived in the 1700s.
So what you have is not a PROBLEM, but rather an exciting discovery - one that might help you break through a "brick wall" someday! Whether it's just a NPE instead, depends on your specific circumstances.
Anyway, be aware that segments can persist for many generations - by sheer chance - and you could be looking at some crazy-distant cousins, mixed right in with your not-as-distant cousins!