By definition VAT is recoverable by all businesses. However in certain States and Associated States, VAT is not recoverable by some institutions or in some circumstances. In many of the older established EU States this has been rectified by bringing income of some, if not all, of these institutions into charge for VAT and therefore the State refunds VAT on expenses. Usually where the VAT is not recoverable by the organisations, notably Universities, they also do not need to collect VAT on fee income.
Unfortunately the Commission does not distinguish between VAT recoverable and VAT which is not recoverable. No indirect taxes can be financed by the EU. In Universities in countries where VAT is not charged on fees and despite the fact that VAT on expenses can not be recovered form the State, it cannot be charged to the EU.
Incidentally the principle is similar to VAT paid on expenses incurred in other States where that VAT cannot be set-off locally, but is still not an eligible expense for EU.