Gaetano Crocco who first suggested the idea of a very short opposition class human mission to Mars using flybys of Mars and Venus in 1956. Crocco Grand Tour See also wikipedia entry: Gaetano Crocco Grand Tour. A similar idea is the basis for the Inspiration Mars proposal.
"Short duration opposition class trajectories have largely been dismissed as a viable alternative for human mission to Mars due to concerns over the increased propulsive requirements, short destination durations, and architecture extensibility. However, a more comprehensive analysis indicates that the relative penalties associated with opposition concepts may not be as severe as originally anticipated. Furthermore, short-stay missions could represent a stepping-stone to long-duration missions, reducing overall campaign risk and allowing for a more progressive build-up of capabilities. The investigation of propulsive requirements, element delivery, and mission risk provides a deeper understanding of the advantages and trade-offs associated with opposition trajectories, presenting new arguments towards their viability as part of a larger exploration campaign."
Trades Between Opposition and Conjunction Class Trajectories for Early Human Missions to Mars
In detail, in section 6, (of Earth--Mars Transfers with Ballistic Capture), they find that ballistic transfer is better than Hohmann transfer for orbits down to a periapsis radius of a little under 30,000 km. That's twice the distance of Deimos.
For the actual savings summarized in table 3, they say saving is about 25% if you want to transfer to an orbit that has closest point to Mars of 200,000 km (about ten times further away than Deimos) of course rare that you want to do that.
The news stories have summarized this as saying that the ballistic transfer gives a 25% saving over Hohmann, but for a close orbit, the Hohmann gives a saving over ballistic.