How to add more combat into an investigation-heavy campaign?

I have experienced such an issue with a previous run of our Fate RPG campaign. The setting is somewhat influenced by the Dresden Files, which means the campaign involved lots of investigation (sometimes railroaded in) as our heroic band of vigilantes and rogue government agents uncovered the sinister plot of the villain.

One of the players did not like that direction and preferred to see more combat. Our GM argued that he is not putting us in combat often because he believes that since character growth comes from milestones rather than smashing mooks over the head, getting into fights often will only use up our Consequences and be a punishment instead of reward. In addition, he pointed out that beating/shooting/fireballing random thugs is likely to complicate the plot as more and more attention being put on the gang of (anti)heroes.

Is there a way to retain the interest of players who want more physical confrontation in an investigation-heavy campaign? None of us are really experienced at DMing a FATE based RPG and I would like some advice before I attempt a campaign with a revised version of the old setting. Do I need to make combat rewarding? Or should I just count on people treating the act of turning a sicario into tomato paste via fireball its own reward? Or is what I am trying to do pointless and it is best for that player to find another game?