  Millisecond pulsars (MSPs) orbiting helium white dwarfs (WDs) in eccentric
orbits challenge the established binary evolution paradigm that predicts
efficient orbital circularization during the mass transfer episode that spins
up the pulsar. Freire and Tauris (2014) recently proposed that these binary
MSPs may instead form from the rotationally delayed accretion-induced collapse
of a massive WD. This scenario predicts that eccentric systems preferably host
low-mass pulsars and travel with small systemic velocities - in tension with
new observational constraints. Here, I show that a substantial growth in
eccentricity may alternatively arise from the dynamical interaction of the
binary with a circumbinary disk. Such a disk may form from ejected donor
material during hydrogen flash episodes, when the neutron star is already an
active radio pulsar and tidal forces can no longer circularize the binary. I
demonstrate that a short-lived ($10^{4}-10^{5}$ \,yr) disk can result to
eccentricities of $e\sim0.01-0.15$ for orbital periods between 15 and 50 days.
Finally, I propose that, more generally, the disk hypothesis may explain the
lack of circular binary pulsars for the aforementioned orbital-period range.
