When managers see things going wrong in a department they may respond by moving staff with key talents to help those who are struggling to cope. Hopefully these specialists will contain the situation and restore normal service, but their talents mean they could be redeployed just as quickly to be of use elsewhere. That can leave the department in the lurch; vulnerable once more, dependent as ever on external capability.
Likewise, it can seem cost effective to bring in external consultants to deal with a specific issue, but if the underlying causes remain then there's the makings of an expensive dependency - unless the required skills can be adopted by the permanent team.
Must it be a choice between getting an expert to deal with an immediate problem quickly, or equipping that department with the right tools and skills it will need to remain robust and reliable? If support doesn't include learning, then how much of a help is it in the long run?