Accusing someone of lying is in effect an accusation of bad faith. An accusation of bad faith is a serious matter, and if you play too freely with it, then you're engaging in bad faith yourself. [1]
The concept of misrepresentation is in a grey area that may or may not have a component of bad faith (see for example the concept of "fraudulent concealment" in courts of equity,[2] the test for which includes a finding of misrepresentation, and note that "fraud" in equity is, confusingly, not at all the same concept as common law fraud), so it's a much more intelligent accusation to make in court unless you have highly probative evidence. [3]
[1] Clean hands doctrine: https://en.wikipedia.org/wiki/Clean_hands
[2] Equity: https://en.wikipedia.org/wiki/Equity_(law)
[3] IANAL
Their central allegation is that they didn't get the information because of Twitter’s refusal to uphold their obligations.
They are claiming breach of contract, and that it looks to them like lying which, if it did happen, might be fraud, but they can't tell, in part because part of the alleged breaches is Twitter not giving them information that might clarify whether the other claims were true or not.