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.