The text you posted is indeed confusing...

But here's what I could find:

The non-taxable legal persons mentioned in the excerpt you posted are "public bodies, organisations, institutions, charities and even individuals if they are not acting in a purely personal capacity" http://www.hmrc.gov.uk/manuals/vatsmanual/vatsm3600.htm . Think charities, public bodies, state schools and hospitals, etc. But not individuals as such.

These entities (a normal business, incorporated or otherwise, will not qualify) will normally be charged domestic VAT in the Member State from which the goods are dispatched, unless in the specific case of "distance selling".

This means that a non-taxable person may acquire goods from other Member States which are subject to VAT in that other Member State up to the value of GBP 77,000 in one calendar year (with effect from 1 April 2012). When this threshold is exceeded, the non-taxable person must register for VAT in the United Kingdom and account for tax on the goods in the United Kingdom as an acquisition.

The same rules should apply to acquiring small enterprises that are below the registration threshold - found many sources from other Member States confirming this, tomorrow I'll try to find a specific confirmation for the UK.

But for now, let's also look at the seller: distance selling or not, or is he maybe a small trader himself (who does not need to charge VAT)?