Compared to mass transfer in cataclysmic variables, the nature of accretion in symbiotic binaries in which red giants transfer material to white dwarfs (WDs) has been difficult to uncover. The accretion flows in a symbiotic binary are most clearly observable, however, when there is no quasi-steady shell burning on the WD to hide them. RT Cru is the prototype of such non-burning symbiotics, with its hard ({delta}-type) X-ray emission providing a view of its innermost accretion structures. In the past 20 yr, RT Cru has experienced two similar optical brightening events, separated by 4000 days and with amplitudes of {Delta}V 1.5 mag. After Swift became operative, the Burst Alert Telescope (BAT) detector revealed a hard X-ray brightening event almost in coincidence with the second optical peak. Spectral and timing analyses of multi-wavelength observations that we describe here, from NuSTAR, Suzaku, Swift/X-Ray Telescope (XRT) + BAT + UltraViolet Optical Telescope (UVOT) (photometry) and optical photometry and spectroscopy, indicate that accretion proceeds through a disk that reaches down to the WD surface. The scenario in which a massive, magnetic WD accretes from a magnetically truncated accretion disk is not supported. For example, none of our data show the minute-time-scale periodic modulations (with tight upper limits from X-ray data) expected from a spinning, magnetic WD. Moreover, the similarity of the UV and X-ray fluxes, as well as the approximate constancy of the hardness ratio within the BAT band, indicate that the boundary layer of the accretion disk remained optically thin to its own radiation throughout the brightening event, during which the rate of accretion onto the WD increased to 6.7 $times$ 10-9 Msun yr^{-1} (d/2 kpc)^2. (Abridged abstract version)