You sound like you are saying you made no mistakes and tried to start them in the same way you always have, but these purchased or traded seeds didn't germinate/sprout as you had expected.
I always doubt myself first because my seed starting procedures are not one set pattern and try varying techniques -- sometimes I can look back and pin-point where I went wrong. Sometimes, it's still environmental because even with the thermostat, the heating mat temperature can be erratic and influenced by the sudden heatwave or chill in weather.
Do you usually start them from your own harvested seeds? I like to experiment and with almost every kind of plants, my own collected/harvested seeds germinate faster and better % than even the purchased or traded seeds from solid commercial and non-commercial sources. This year, I have had surprising number of failures from traded seeds even though the gardeners who sent them are reporting good results with their own seed starting (and I have a fair confidence in the starting procedure used for these particular seeds). We have speculated that the postal system might be doing something -- irradiating mail, etc. I have heard that this can happen more if the particular envelope went through certain mail sorting hubs.... OK this is PURE SPECULATION or as You say GUESS.
...are you trying to decide whether to make a claim of seed failure to the person or company you obtained the seeds from? If you have some left, you may want to try the simple paper towel in a baggie/zip bag technique -- I prefer to use what I call "spoon seedzip" technique -- and observe what % the seeds will actually GERMINATE....
Hmmm looking back to your descriptions, you mentioned that some of them germinated but failed to sprout (tried to sprout but failed to make their way above-"ground") -- that part could be because the seeds were sown too deep (were the hypocotyl extraordinarily long?) or else they got dried out after germinating (hm. Did you say they had cotyledons but NO roots? I was going to ask about condition/appearance of their roots). I have no definitive ideas about the coiled roots, so I won't guess without more details (photo might help).