From the Revenue Leaflets & Guides Chapter 9 Invoices, credit notes etc.
"Traders who issue invoices and credit notes, and persons to whom these documents are issued, should ensure that the documents accurately represent the transactions to which they refer. Failure to do so may have serious consequences for all parties concerned. If, for example, a wholesaler issues an invoice describing as zero rated, goods which are in reality taxable at the standard rate of 21%, the wholesaler is nonetheless liable for VAT at the 21% rate and also by his or her action is open to prosecution."
It is the duty of the seller to collect VAT on behalf of the state. If it wasn't charged and the customer doesn't opt pay up then the seller would still be liable.
Of course that is the 'worst case scenario' for the seller.
In reality and from what has been posted here the customer seems somewhat willing to pay but with certain conditions.
It shouldn't 'cost' the customer.
So the original question was
Well, in the end, NO! because if you pay the VAT invoice you can reclaim the VAT paid. Technically no cost to you.
Will it cost you? Well if you pay the invoice immediately and wait for the reclaim then yes!
The VAT should be invoiced by the seller. The customer should reclaim. The seller should wait until the reclaim is paid before looking for payment. If that sparks an audit for the customer the seller should foot the bill(s).
The seller is on very thin ice.
The Revenue guide continues: "The retailer is likewise liable at the 21% rate of VAT on the subsequent supply..."
QUESTION TO OP: Did you charge VAT on the goods when reselling? If not you could be up the creek and relying on your customers to cough up your VAT liability...