I think the real issue here is the company, and this is independent, to some degree, to the fact that you may have been inefficient or not.
A sane company should provide sane feedback.
This means that:
it should not be based on hearsay
it should never present generic/vague accusations, but detailed description to which the problem is and a proactive ...
I explained that I only send emails for action items which are someone’s job and that I can not action myself.
One way to read this is that you never emailed anyone except to order them to do something.
I never asked a question via email, nor had a conversation via email, nor brainstormed a solution via email.
Is it possible that you simply didn't ...
I don't know what more to advice than to address those people blame.
In few of my previous jobs such things was called "Extracting the weeds". There are people who make their job blaming others. They don't do anything they were hired for, just try to find people on whom the can put blame for not doing their task.
Some companies are aware that in the process ...