Something similar is possible if you use IE to download from FTP server:
FTP protocol normally uses two connections, first is control channel for FTP commands and second data channel to send the actual data. In active mode FTP client creates a local listening socket and sends PORT command to FTP server specifying local IP address and port. Then FTP server connects this IP:port and requested file is transferred over this TCP connection. Thus request for file is sent over one TCP connection but file is sent over another one. In passive mode both control and data channels are initiated by FTP client (this mode is easier for NAT traversal), but once again request is sent by client over control channel but data are sent from server over data channel. This is very similar to what you have reported. If I remember fine normally IE uses FTP in passive mode.