Does a Passive House have to have thick walls?

Generally, yes. A Passive House Building needs more insulation than a typical building, and this is generally achieved by having significantly thicker walls. The thickness of walls depends on the U-values required which in turn is greatly dependant on the performance of the insulation, the type of construction (whether concrete, timber frame, etc), overall design, orientation, compactness and so forth. You generally won’t notice the thick walls from the outside of the house, however, as the windows are placed in the insulation layer which is best placed towards the exterior of the building shell.