  Several tens of massive binary systems display indirect, or even strong
evidence for non-thermal radio emission, hence their particle accelerator
status. These objects are referred to as particle-accelerating colliding-wind
binaries (PACWBs). WR 133 is one of the shortest period Wolf-Rayet + O systems
in this category, and is therefore critical to characterize the boundaries of
the parameter space adequate for particle acceleration in massive binaries. Our
methodology consists in analyzing JVLA observations of WR 133 at different
epochs to search for compelling evidence for a phase-locked variation
attributable to synchrotron emission produced in the colliding-wind region. New
data obtained during two orbits reveal a steady and thermal emission spectrum,
in apparent contradiction with the previous detection of non-thermal emission.
The thermal nature of the radio spectrum along the 112.4-d orbit is supported
by the strong free-free absorption by the dense stellar winds, and shows that
the simple binary scenario cannot explain the non-thermal emission reported
previously. Alternatively, a triple system scenario with a wide, outer orbit
would fit with the observational facts reported previously and in this paper,
albeit no hint for the existence of a third component exists to date. The
epoch-dependent nature of the identification of synchrotron radio emission in
WR 133 emphasizes the issue of observational biases in the identification of
PACWBs, that undoubtedly affect the present census of PACWB among
colliding-wind binaries.
