It seems like a massive grey area really. 
Its only a grey area because of miss information supplied, if you talk to the Post Office, DLVA and your Insurance Co they will probably tell you, you need Insurance in place to Tax, and the System will check for Insurance on a Data Base at the time of the Tax application, it probably did or still does, the problem was on the old system there was so many vehicles with Insurance in place but not showing on the system, mainly due the Data Base relied on the Insurance Companies or Brokers to update the System which could take anything from 12 Hours to 5 Days to show up, The Post Office / DVLA could then by-pass this by proof of Insurance being presented at the time of application.
The next issue came with the introduction of No Tax Transfers of Sold Vehicle anymore, The DVLA needed a 'No Excuse Tax It before You Drive It' policy in place to Enforce this, so the System was set were you could effectively Tax your Car at 3 o'clock on a Sunday morning if need be, by either Telephone or Online, so in order to achieve this the Insurance Check was suspended and only correct Vehicle detail info (Log Book) and Mot was the requirement. In fact they suspended the Insurance check about a year before the new Tax rules came out back in 2013 but that wasn't common knowledge.