A shop may avoid displaying a full serial in public photos to reduce misuse. That is different from refusing to let a serious buyer verify the identifier before purchase.
Ask for a controlled verification
The shop could show the serial in person, provide it privately for a check, or arrange an independent inspection. Agree how the result will be documented and whether the serial can be included on the invoice.
Match the sale documents
Ask the invoice to identify the specific watch and record its serial accurately. Compare it with the physical engraving before payment. If the shop cites privacy, discuss a practical approach that still lets you verify the piece.
Decide based on the response
A reputable seller should explain its process and allow reasonable due diligence. If it will not provide any way to confirm the serial or puts pressure on you to buy first, you can walk away.
A search result can help screen status, but it does not authenticate the watch or settle title. Keep those questions separate.
Get an Item-Specific Check
Verify the exact serial privately and keep it on the purchase record.