STURP was never sanctioned by the Vatican. They managed to get permission to view the Shroud from the Duke of Savoy, then in exile as the ex-king of Italy, who was its owner until his death in 1983 when he bequeathed it to the Vatican. So far as I can see the Vatican has always kept its distance from STURP, certainly they have turned down any attempt by STURP to become involved in further testing. This is hardly surprising as no one in the STURP team had any experience of dealing with ancient textiles- there does not even seem to have been an expert conservationist with them to offer advice when they examined the Shroud.
The Vatican assumed ownership of the shroud in 1983. The C14 testing was finally agreed and done at the end of 1988, and published early in 1989 (iirc).
So throughout most of the years of those discussions, the Vatican was the owner of the shroud.
In those years of discussions leading up to agreement on performing the C14 tests, the participants who took part in the discussions were certain representatives of the C14 labs (inc. the aforementioned Harry Gove, who wrote a lengthy book drawn entirely from the contemporaneous notes which his secretary took at all the meetings), various Catholic church representatives inc. most notably Luigi Gonella who was by then the Vatican's appointed main keeper of the shroud in Turin, and iirc from Gove's book, various members of STURP.
The point is this - it is very clear from Gove's book (assuming his contemporaneous personal notes and his recollection of meeting and dealing with all these church officials and members of STURP are true and correct ... for which, see his book), that Luigi Gonella in particular, but also in concert with various other Catholic church officials in and around those 10 years of meetings, was very friendly and familiar indeed with a number of members of STURP who also attended those meetings and made their representations about how any C14 should be done, who should do it, how they should do it etc. etc.
If Gove's account is anything like true at all, then it is perfectly obvious that Gonella, certain other church representatives who Gonella was working with, and the members of STURP who were all at those meetings in Turin, were constantly trying to dictate what should be done if anything at all was to be done by any C14 tests.
And in case it's not obvious what has that to do with the Vatican, the Pope, and the Catholic church in Turin or Rome - by that date the Vatican and the Pope as it's head, had become the owners of the shroud, and were therefore in charge of what Gonella and STURP could or could not do at any meetings deciding anything about investigative access to the shroud. And even before that date of 1983 when the Vatican officially took ownership of the shroud, the shroud was kept in Turin where Gonella was the main, and very senior religious employee in a catholic Church of which the Pope and the Vatican cardinals are the head ... Gonella, the archbishop of Turin and their various religious officials could not do anything unless the Vatican ultimately agreed to it.
No doubt the Pope and the Vatican always wanted to distance themselves from any controversies surrounding objects such the Turin Shroud. And certainly they tried to play down the results after the C14 dates were announced. But the bottom line is that the Vatican, the Pope and it’s Cardinals are the head and the authority of all Catholic churches in Italy, including the bishops of the church in Turin and it’s senior religious officials such as Luigi Gonella as their keeper of the Shroud. So Gonella, the bishops and the Vatican are certainly all responsible for their not inconsiderable involvement with allowing numerous members of STURP to keep having uniquely privileged access to conducting experiments on the shroud for 20 years prior to the C14.
