1. A method comprising: identifying one or more proxies in a storage management system that are eligible to back up a given virtual machine in a first set of virtual machines in the storage management system, wherein any one proxy among the one or more proxies represents one of: (a) a first virtual machine that executes on a first computing device, wherein the first virtual machine executes a data agent for virtual-machine backup, and (b) a second computing device that executes a data agent for virtual-machine backup; wherein the identifying comprises: (i) determining (A) a set of candidate proxies that are candidates to back up the given virtual machine, and (B) a mode of access available to each respective candidate proxy for accessing the given virtual machine's data as a source for backup, wherein the mode of access has a predefined tier of preference; (ii) classifying each candidate proxy in the set of candidate proxies based on the predefined tier of preference for the respective candidate proxy's mode of access to the given virtual machine's data as the source for backup; and (iii) defining one or more candidate proxies that are classified as having the highest-tier of preference as being eligible to back up the given virtual machine; and wherein the identifying is performed by a first data agent for virtual-machine backup that operates as a component of the storage management system.