Flux transfer events (FTEs) are transient phenomena frequently observed at the Earth's magnetopause. Their usual interpretation is a flux rope moving away from the reconnection region. However, the Magnetospheric Multiscale Mission revealed that magnetic reconnection sometimes occurs inside these structures, questioning their flux rope configuration. Here we investigate 229 FTE‐type structures and find reconnection signatures inside 19% of them. We analyze their large‐scale magnetic topology using electron heat flux and find that it is significantly different across the FTE reconnecting current sheets, demonstrating that they are constituted of two magnetically disconnected structures. We also find that the interplanetary magnetic field (IMF) associated with reconnecting FTEs presents a strong By component. We discuss several formation mechanisms to explain these observations. In particular, the maximum magnetic shear model predicts that for large IMF By, two spatially distinct X lines coexist at the magnetopause. They can generate separate magnetic flux tubes that may become interlaced.