Les doesn't say the excess is exempt. He is only explaining what payments will be made.
If the insurance company was collecting the excess, then it would be a simple case of invoicing the insurance company for the full £2000 plus VAT and leaving it to them to sort out. This complexity is due to the insurance company (and the insured party) asking the service provider to perform a more complex debt collection exercise.
The overall position has to be a payment to HMRC of 20% on the cost of the service provider performing the work (£2,000 @20% = £400).
You could argue that technically you could perform the same process that I applied to the the VAT Registered Entity to the Non VAT Registered Insured Party (as follows), but I was trying to give what I felt like the simplest solution for the service provider.
So the alternative for the Non VAT Registered insured party would be:
Invoice 1, Line 1 - VAT invoice to Insurance Company for full fee (£2,000 + £400 VAT using a 20% VAT code) including naming the Insured Party as the beneficiary of the service
Invoice 1, Line 2 - Credit on the invoice to insurance company showing the EXCESS recovered from the Insured Party (£250 using an exempt VAT code so that the credit isn't included on the VAT MTD return)
Invoice 2 - "Invoice" to Insured Party for £250 using an exempt VAT code (so that the income isn't double counted but the value shows on your sales ledger).
This comes out with the same result and has the added benefit that you are proving that you are only expecting the insurance company net of excess but seems slower for the service provider to process. It's all a matter of personal taste.
Les' initial point on the VAT registered client only paying the excess plus VAT, is correct, but my response in this thread takes into account that most accounting systems cannot produce a "VAT only" invoice, on the basis that if there is no taxable supply then there is not VAT.
The solution I have given shows the right taxable supplies, and endeavours to ensure that the "debt collection" reallocations between the insurer and the insured are ignored within the MTD VAT Return.
NB Exempt is not the same as zero rated.