That doc is dated 2003 so I guess the regs have changed (and there have been some pretty major changes recently like CA2006 and FA2011). I certainly don't get VAT invoices from the US suppliers I use (linode and digital ocean for example).

Edit: The 4th paragraph here seems to settle it: http://www.hmrc.gov.uk/manuals/vatpossmanual/vatposs14300.ht...

The reverse charge mechanism places the burden for accounting for VAT on the recipient if the supplier is outside the UK.