No oil majors are using nowadays the term ‘acceptable’ or approved, as a vessel is always screened prior to use, instead, at the end of screening process, major may only respond that ‘no further information required at this time,’ which usually can be considered as the completion of a vetting procedure.
BS & N LTD (BVI) v Micado Shipping (Malta) (The Seaflower)  1 Lloyd’s Rep 341 per Rix LJ at para 64:
An oil company’s approval may reflect the vessel’s condition, but it is a matter of status rather than condition. Similarly, a vessel’s class is a matter of status – although that status may be affected in many different ways: at one extreme a vessel may be completely out of class, which is a most serious matter, because such a vessel cannot trade, but at another extreme there may be only a recommendation or even a mere notation of class that something relatively minor be attended to within a certain date. In the case of an oil majors’ approval, however, the vessel either has it or it does not. In that respect it is like a term as to the vessel’s class at the time of contract: if the vessel is out of class, the condition as to her class is broken. As for unseaworthiness, it seems to me that there is no proper analogy at all between that and an oil major’s approval; and unseaworthiness is not a matter of status.
By His Honour Judge Mackie QC Transpetrol Maritime Services Ltd v SJB (Marine Energy) BV  EWHC 3374 (Comm) at paras 7, 29-30:
7. Oil majors operate a system of vetting and approvals to ensure that the vessels they use or trade or buy cargos from are of satisfactory quality. The companies pool their inspection reports made for the purposes of approvals through a database know as SIRE. The inspections cover the same or similar matters for all companies. A report is sent to Owners who may respond with comments. When Owners provide comments these are incorporated in the SIRE report which is then available for all SIRE members to read. Vetting involves more than simply looking at the SIRE report but that report is a major factor in any decision. It became clear from the evidence that the owners and operators of tankers seek and collect written approvals from oil majors and like to have as many as possible, preferably from the top names. Approvals greatly help marketing.
29 … "approved" was used in the market in 2007 to mean "acceptable to" oil majors who might or might not, when the prospect of a real transaction arose, decide to approve that vessel for use or as a suitable carrier of cargo to it. This means that it is unnecessary to examine closely the considerable amount of necessarily somewhat imprecise material and evidence on that point.
30. It seems clear from this evidence that it is not the practice of oil majors to grant approvals as such in advance. Indeed letters from the companies relied upon as approvals will generally state that no such approval has been granted and should not be assumed. This is the result of reluctance by oil majors to commit themselves about a vessel in advance following the problems caused by pollution incidents involving the Erica in 1999 and the Prestige in 2002. A report that these vessels had been "approved" by oil majors had led to damaging publicity.