The background to how this message appears is important to understanding why this is.
It is displayed when the guard has informed the Control that the service is full and standing. It isn't then removed again unless the guard reports that the train is no longer full and standing.
Consequently if the train is reported as full and standing leaving Ely, but a large percentage get off the train at Peterborough as they do, unless the Control are told otherwise the "very busy" message will be shown for the rest of the journey even if the train isn't.
It is quite easy to overlook when you're busy and particularly when there is a crew change en route.
Thanks for that explanation which confirms that my decision to ignore such messsges is a good one. More importantly though, if the message has a good chance of being incorrect and likely to mislead people it is, in my view, better not used at all as demonstrated here:
Last year we were waiting at Leicester for an early evening EMR train to Sheffield which was being flagged as a full 5 car. It turned up with two units, the front almost empty which we boarded. The refreshment trolley got on that and we got welcome coffees.
At Sheffield an unrefreshed hoard got off the crowded rear unit including a football team and supporters.
Good intentions but not too helpful outcomes.
and again with my experience at Leeds the other evening, albeit with an incorrect announcement (might have been on the screens as well, I had no need to check):
I was heading for the Northern semi-fast to Sheffield (due to depart 2 mins before the XC Edinburgh - Plymouth service but arriving around 15 mins later in Sheffield) on the basis that I would far more likely get a seat on that. However as I reached the overbridge an announcement for the XC advised passengers for stations beyond Bristol to Plymouth to board the front 5 coaches as the rear coaches would be detached at Bristol - ah good, at least 9 coaches then with an almost certain seat if I headed to the far end of the platform, which I did.
The train arrived and I was surprised to see the front carriage already full and standing and a crowd heading up the platform towards me. The surprise disappeared when I realised the train was only 5 coaches and the mythical second set was just that
(it had presumably been only one set from Edinburgh and definitely from Newcastle, so plenty of time to get the announcement correct). By then it was too late to retrace my steps and get over to 17B in time for the Northern train I had been aiming for originally and not wishing to travel on the grossly overcrowded XC I waited for the next Northern semi-fast.
Lesson learned, I will be treating verbal as well as displayed messages linked to train capacity with a pinch of salt in future.