It is not true that they are unable to display a group booking unless the agent has a sign limited them from doing so - which would be rather unusual. My guess is that either procedurally they won't do this, or that the agent has not been properly trained.
A group booking in BA will have, as Hartington says, a 6 character record locator. There will be a group name when the booking is created, for example 30BARCELONATOUR and as the individual names are assigned the unassigned group name will change, so if we add Mr and Mrs Smith, to use a very original example, then it will become 0.28BARCELONATOUR and 1.1SMITH/FRED 2.1SMITH/ANNE. Normally 30 days before departure the names are required so the group name becomes 0BARCELONATOUR and there are 30 individual names.
In the passenger list, the group name in displayed with a G next to it and the individuals comprising the group are displayed with an N next to them.
The original record locator remains the same unless passengers are split off.
In order to retrieve Mr. Smith, who is part of that group, the agent only needs to make the normal retrieval entry, comprising flight number, date, and name, and it will retrieve the group PNR of which he is part. Therefore, what you have been told is
