I guess you can look at it from the other side. If your three explanations are
1: Patient's dead
2: Monitor failure
3: The tube is not in the trachea.
If it's #1, it doesn't matter to me if that patient is bagged or has an ET tube in, they aren't coming back. If I remember right no one get successfully revived if their ETC02 is bellow a certain number (7? 5?, something like that. Either way 0 is less that that threshold). So that tube doesn't really matter in that case.
If the truth is number 3, clearly the tube should get pulled.
If it's number 2, ideally there should be another monitor available (ie the condition boss's) that can be tried.
Given the reduction of importance of intubation in ACLS, it worries me a little if a lot of time and effort on the code are being spent trouble shooting this tube. In the ER if there is bad CO2 we pull the tube, even if their are good breath sounds.
If I were a medical director, thinking on a system level, it would make me a little nervous keeping a tube in with a C02 of 0. I'm sure you and your partner are very good medics, but there are a lot of guys out there who are just over the competency line and who I could see arguing that they are sure a tube is in, when it in fact isn't. I think I'd rather have 10 or even 20 tubes taken out that were really in, rather than have 1 patient transported with an esophegeal tube.
Final thought is if you have a 3rd C02 line, blowing into the monitor during the code to confirm that it isn't a monitor problem, and documenting that on your run form so if someone looks at the strip they don't think there was ROSC. If you did that during the call you know it's not the line and it's not the monitor, so you are left with options 1 and 3. Either way leaving the tube in doesn't help the patient, and if 3 it will hurt them.
How did the patient do?