Simple models of fluid and solid mechanics predict that the depressurization of a shallow reservoir that occurs during large effusive eruptions produces exponential trends in time series of both pressure drop and extruded volume. These models are attractive due to their simplicity and because they can explain geodetic and extruded volume data recorded at several volcanoes like at St. Helens and Cordón Caulle, regardless of their magma compositions. However, several lava and dome-forming eruptions like at Redoubt, Hekla and Santiaguito volcanoes do not show clear ground deformation coeval to lava and dome effusion despite the extrusion of at least 0.1 km3 DRE of magma. This apparent paradox can be explained by a variety of factors including deep magma sources and highly compressible magmas that leave no geodetic footprint. Here we explore the role of magma buoyancy with a reanalysis of ALOS-1, TerraSAR-X and RADARSAT-2 InSAR ground deformation and Pleiades DEM data of the VEI 5 Plinian and dome forming rhyolitic eruption of Chaitén volcano in 2008-2009. We show that almost all of the recorded ground deformation occurred during the first three weeks of the eruption, which implies that the extrusion of a rhyolitic dome (~0.8 km3 DRE) did not result in significant depressurization of a magma reservoir, despite the clear exponential trends in the extrusion data. Instead, we show that the exponential trend in the time series of extruded volume can be explained by magma ascending due its buoyancy instead of its overpressure. These results imply that ground deformation alone is not always indicative of the temporal evolution of an eruption and urges for the acquisition of denser time series of DEM data to calculate time-lapse extrusion rates.