Machavity’s point #1 is a good explanation, but I don’t think point #2 is on the money. Although VPNs might not have been as common in 2008, remote access was definitely well established. I was personally using ssh as far back as 1999 for remote access to my employer’s computers, and an ISDN connection as far back as 1995—and I’m no billionaire. Tony Stark would for sure have had remote access to Stark Industries’ internal network.
However, the files to be copied were very large. Transferring them over Tony’s remote connection would probably cause a large and sustained increase in the connection’s bandwidth metrics. Stark Industries’ IT security staff would have a network dashboard with a graph that would make the increase obvious, and the increase might trip alarms.