Apply transforms to linked objects? Note:
Vader's solution set me on the right track, but I ended up using this, as it goes a bit faster with large numbers of objects.

Original question:
Is it possible to directly apply transforms on linked object data? Blender does not seem to let you do this. It results in an error: Cannot apply to a multiuser: object, object2, etc. aborting
That makes sense, but I should be able to apply the scale to all of the objects, right?
For instance, I have three cubes which are linked, but have different scales:

I realize that because the mesh data is linked, they all have to be the same size once the scale is applied.
I tried selecting them all with the smallest cube active, then applying the scale.

The expected result is that they all become the size of the smallest cube with scales of 1,1,1:

However, it just throws the same error instead:

Is there some way to do this without unlinking everything and then relinking?

Update: There seems to have been some confusion about if this was possible or not, so I'll quote my comment below to help clarify what I wanted:

I only want the active object to remain the same size, I realize the other objects will have to become the same size as the active object. I don't see why that would be impossible..
Vader's solution works, but I think this modified version is slightly more efficient because it only unlinks the active object:

import bpy

selected=[]
# de-select all selected objects and add to array:
for obj in bpy.context.selected_editable_objects:
    selected.append(obj)
    obj.select = False
# reselect active object
bpy.context.object.select = True
# Make single user and apply scale
bpy.ops.object.make_single_user(type='SELECTED_OBJECTS', object=True, obdata=True, material=True, texture=True, animation=True)
bpy.ops.object.transform_apply(location=False, rotation=False, scale=True)

# select objects again
for obj in selected:
    obj.select = True
    # reset scale
    obj.scale = 1,1,1
# link selected to active
bpy.ops.object.make_links_data(type='OBDATA')