Later in this episode, Izzy is making a Digital Barrier, following instructions from Gennai. He links his lap-top up to his parents' PC, and the PC shows a chart, showing how long it will take for the Digital Barrier to be in place. Tentomon says that it should work a lot faster, and Izzy then says,"Yeah, I've been telling my Dad to get me a faster modem!"
BUT...Izzy is not using his modem! He is using a cable to connect the two computers!(the cable is called a NULL cable, I think.) And he can't have connected to the Internet in the process, because you see everything that happens. Izzy accesses Gennai's program through the cable, and not once does he open any other application.