We present the analysis of four candidate short-duration binary microlensing events from the 2006-2007 MOA Project short-event analysis. Three of these events are determined to be microlensing events, while the fourth is most likely caused by stellar variability. One of these events, MOA-bin-1, is due to a planet, and it is the first example of a planetary event in which the stellar host is only detected through binary microlensing effects. This is one of the most massive and widest separation planets found by microlensing. The scarcity of such wide-separation planets also has implications for interpretation of the isolated planetary mass objects found by this analysis. In particular, if the entire isolated planet sample found by Sumi et al. consists of planets bound in wide orbits around stars, we find that it is likely that the median orbital semimajor axis is <30 AU.