You have almost got it right. The referred article is saying (if you read some of the examples, which do make it clearer) that if you have consent of your customer (client) to recharge expenses, then you book the entire expense to purchases and then the entire cost (including VAT where charged) to the disbursement element on your invoice. The important element is that if VAT is charged in the original cost, then you do NOT reclaim the VAT but you recharge it to your customer included in the total cost.
