She is correct
The question at hand is, whether or not Eldritch Blast is considered, as a spell, to have multiple damage rolls, or if it just has multiple attacks that happen to have their own separate damage rolls.
A similar issue comes up with Scorching Ray (shoots several fire beams, each with their own attack) and the Sorcerer feature, Elemental Affinity.
Elemental Affinity states that it only applies to a single damage roll, and Jeremy Crawford has explained that Scorching Ray is considered to use multiple damage rolls.
If Scorching Ray (which is functionally identical to Eldritch Blast) is considered to use multiple damage rolls (and only gets a single bonus from Elemental Affinity), then that means Eldritch Blast also uses multiple damage rolls.
The difference is, Elemental Affinity only applies to a single roll, where Empowered Spell is allowed to work on multiple rolls. You made the correct call on letting her apply it.
This seems to be fine, since it does not guarantee a better roll. On a max level Eldritch Blast, assuming each blast hit, it would deal an average of 5.5 per hit, 22 damage total from rolls, and a minimum of 4. We could assume that she's dealing less-than optimal damage. That's about 0-14 points of damage that she's roughly going to get from an optimal use.
Compared to Toll the Dead (also a Warlock spell), which would deal 26 from rolls, and could be Twinned for 2 sorcery points to 52 damage if neither attack misses.