Can anyone please -
1) advise if there is any truth in what he has been told?
There is a grain of truth but its been completely garbled.
If your friend has by chance been infected by a virus or malware, or is downloading using bittorrent or similar then they might have lots of connections open, and closing them would speed up web browsing/email.
If your friend is a typical user who uses email/web, then a handful of connections shown in netstat is normal and just how the internet works. (e.g. a web browser loading a site such as BBC News can open quite a lot of connections to get all the pictures and text. They are closed after a while).
Your friend needs to check he has the Sky router in the master socket, and preferably has any wired in extensions removed (plugged in is fine if they are AFTER the filter). If that is already the case then check for a broken filter.
Technical information from the Sky router would be useful too.
James BT Infinity 2 19/09/2012 - Estimate 44.6/6.5 - Install 52/12 - Actual 46 / 8 Mbps
13 years of broadband - ntl:(512k/1M)/BTbusiness(2M)/Metronet(2M)/Bulldog(8M/16M)/BE(16M)/BT FTTC(50M)