This seems easy to test now that United has asserted that your balance of 1,8xx,xxx is correct. Take a United-operated flight, wait for the miles to accrue to your account online. Check whether your balance is still 1,8xx,xxx or is something higher.
If your balance is still 1,8xx,xxx after you take another flight, write back again and ask whether they were wrong before or are wrong now.
In my experience the lifetime mile counter shown online increments at the same time that the miles post to my account (I don't see them growing separately).