"Would this still be clear bad faith had these chat logs not been created?"
Yes, almost certainly. The party claiming non-compliance has to prove your non-compliance, but they do not have to prove your bad faith.
Instead, the burden falls to the enjoined party to prove good faith.
Affirmative good faith usually comes up more in trying to dissolve injunctions, etc (where the enjoined party has to prove good faith) than civil contempt of an order.
This is because in the case of civil contempt, Judges still have discretion to find you in contempt even if you acted in good faith. IE bad faith will definitely get you contempt, but good faith alone will not save you from it. You can act in good faith, not do enough, and still be found in contempt for not doing enough. This helps dissuade malicious compliance as well.
"The absence of willfulness does not relieve from civil contempt. Civil as distinguished from criminal contempt is a sanction to enforce compliance with an order of the court or to compensate for losses or damages sustained by reason of noncompliance . . . . Since the purpose is remedial, it matters not with what intent the defendant did the prohibited act . . . . An act does not cease to be a violation of a law and of a decree merely because it may have been done innocently. The force and vitality of judicial decrees derive from more robust sanctions. And the grant or withholding of remedial relief is not wholly discretionary with the judge. . . . The private or public rights that the decree sought to protect are an important measure of the remedy."
Yes, almost certainly. The party claiming non-compliance has to prove your non-compliance, but they do not have to prove your bad faith.
Instead, the burden falls to the enjoined party to prove good faith.
Affirmative good faith usually comes up more in trying to dissolve injunctions, etc (where the enjoined party has to prove good faith) than civil contempt of an order.
This is because in the case of civil contempt, Judges still have discretion to find you in contempt even if you acted in good faith. IE bad faith will definitely get you contempt, but good faith alone will not save you from it. You can act in good faith, not do enough, and still be found in contempt for not doing enough. This helps dissuade malicious compliance as well.
See, generally, mccomb and friends:
https://supreme.justia.com/cases/federal/us/336/187/
"The absence of willfulness does not relieve from civil contempt. Civil as distinguished from criminal contempt is a sanction to enforce compliance with an order of the court or to compensate for losses or damages sustained by reason of noncompliance . . . . Since the purpose is remedial, it matters not with what intent the defendant did the prohibited act . . . . An act does not cease to be a violation of a law and of a decree merely because it may have been done innocently. The force and vitality of judicial decrees derive from more robust sanctions. And the grant or withholding of remedial relief is not wholly discretionary with the judge. . . . The private or public rights that the decree sought to protect are an important measure of the remedy."