What kind of update is he supposed to be getting? If neither the doctor, nor the player, know when he'll be recovered, how do you provide an update on something you don't know? It's not like his return is easily identifiable or scheduled.
Should they be suspicious? No, not really. What's clear is that there's two things fans are doing wrong:
a) they're taking any timeline from literally anybody as gospel. Like most of the baseline for what people were expecting didn't come from John or literally anybody within the organization. It came from guys like Adam Schefter, who tweeted out ranges for the injury based on how others with similar, but not identical injuries, have had.
b) fans have zero ability to deviate off those timelines, or even comprehend the fact that information might change. Basically, they've never had these types of injuries, so they think anybody who takes longer than what somebody else said they should is either a pussy or milking it.
So I understand why fans are suspicious, but it doesn't mean that suspicion is based on literally anything, other than pure ignorance. They just heard what somebody said, took it as gospel, and expect that nothing would change in the meantime.
As somebody who hasn't had Lamar's injury but has torn their ACL before, among other injuries, like broken bones, I can tell you I missed the "timeline" for recovery by many weeks in some cases and months in others. And not once did I think "man the doctor didn't know what he was doing".