An antenna has an equivalent impedance both in transmit and in receive. If the load in receive mode is matched to that antenna impedance then there is no reflection from that load back out the antenna, the incident energy on the load will be completely absorbed. Note the emphasis on energy incident on the load not on the antenna. The actual reflectivity of an antenna will depend on the incoming direction of the wave, for example.
Whether the load is matched, therefore, just concerns the load and the way it is connected to the antenna ports via a transmission line, that is a matched load for one incident direction maybe mismatched for a different one. This problem does not show up in transmission mode because there is only one way and one transmission line mode used that the source energy may excite the antenna ports. (This is the main reason why antenna designers calculate the resulting antenna pattern in transmit mode instead of analyzing it in receive mode, by reciprocity the transmit and receive antenna patterns are the same.)
Following @JanLalisky perfectly correct answer I would like to add that the physical reason for the secondary emissions from a receive antenna is because the incident wave is usually emitted from a far away source so it is either spherical or planar. In either case it is not the type of EM field that a "perfectly matched" antenna would emit in its transmit mode. For example, around the antenna there is a reactive field (non-radiating) that would have be recreated by the incident wave so the antenna metal not reradiate parts of it in some unknown directions, a simple plane wave cannot do just that.