Yes... that's exactly how it works. There's no SCHEME in conspiracy terms.
I buy product X at £1000 + VAT = £1200
I sell product X at £2000 + VAT = £2400
I have charged £400 VAT and I have paid £ 200 VAT. I give the HMRC £200 (£400 for the VAT collected minus the £200 I paid).
In the EU, to save complex to and from between different Tax offices in different countries, if you have a VAT number the foriegn company does not charge you VAT. In the small chance that there is an error and they do, you reclaim it back like you would do normally, as per above.
If I change the example...
I buy product X at £1000 + VAT = £1200
I sell product X at £500 + VAT = £600
I have charged £400 VAT and I have paid £ 200 VAT. The HMRC gives me £100 (£100 for the VAT collected minus the £200 I paid).
If you are not VAT registered, you pay VAT from the EU countries at their rate like you would do here.
There is nothing personal in this, you do not understand how VAT works. Which is quite surprising for someone who is VAT registered. But it is no different for any business. The rules apply to all. Both ways. We do the opposite when we deal with our EU clients.