We estimate the low-frequency internal variability of Northern Hemisphere (NH) mean temperature using observed temperature variations, which include both forced and internal variability components, and several alternative model simulations of the (natural + anthropogenic) forced component alone. We then generate an ensemble of alternative historical temperature histories based on the statistics of the estimated internal variability. Using this ensemble, we show, first, that recent NH mean temperatures fall within the range of expected multidecadal variability. Using the synthetic temperature histories, we also show that certain procedures used in past studies to estimate internal variability, and in particular, an internal multidecadal oscillation termed the "Atlantic Multidecadal Oscillation" or "AMO", fail to isolate the true internal variability when it is a priori known. Such procedures yield an AMO signal with an inflated amplitude and biased phase, attributing some of the recent NH mean temperature rise to the AMO. The true AMO signal, instead, appears likely to have been in a cooling phase in recent decades, offsetting some of the anthropogenic warming. Claims of multidecadal "stadium wave" patterns of variation across multiple climate indices are also shown to likely be an artifact of this flawed procedure for isolating putative climate oscillations.