This hand cropped up yesterday in the final of the Tollemache Cup (EBU Inter-County teams of 8) in the match between Cambs & Hunts (of which I was the N-PC) and Surrey (for whom regular BBOL Laws Forum contributors Jeffrey & Frances were playing, though they were not directly involved on this hand). The final double in the hand diagram might have been East's rather than West's but nothing turns on that.
NS are a fairly regular partnership and play quite a lot of "stuff". 1♥ by N was alerted by S and explained (I'm not sure whether at the time or before the opening lead) as showing ♠, hence S's 3♠ bid. N had UI from the alert; whether he realised at the time that his bid, systemically, showed ♠ or merely that NS were not on the same wavelength I am not sure, but nothing turns on that, either. EW reserved their rights and, at the end of the hand (when they had allowed 3NT to make though it can be beaten) asked for a ruling first on whether the 1♥ bid had been correctly alerted and described and secondly on N's 3NT bid.
This was the penultimate match of the final (an eight team all play all over 14 boards affair with each NS pair IMPing with each EW pair) and matters were slightly complicated by the fact that one of NS had to leave immediately after this penultimate match to catch a plane to Hong Kong and the other one was driving him to the airport. However, before leaving, they gave a copy of their convention card to the TD and explained that they don't play splinters in many sequences and that this was not one of them.
The TD came to see me during the final match, explained the facts and that his decision (after consultation on the second point) was that the table result would stand - first because the convention card clearly showed that the 1♥ bid showed ♠ and secondly because he didn't think N had a logical alternative to 3NT.
Looking at the NS bidding in isolation, without reference to N's actual hand, at least a substantial number would think that 3♠ by S could only be a splinter bid agreeing ♥. However, if N is also entitled to have regard to his own ♠ holding and to the opponents' bidding (or lack of it) 3♠ is very unlikely to be a splinter because in that case EW (not shy in the bidding, as NS knew) had at least ten ♠ between them and yet had not overcalled the suit over 1♦ or bid it in response to the T/O double. I think N said that 2♠ by S over 2♣ by E would have been NF so that, a natural, forcing, 3♠ bid (putting the UI to one side) was a logical alternative.
At the end of the event, the medal positions were such that an adjustment of the result to 4♥ - 1 (whether or not doubled) would have been sufficient for my team to finish in the bronze medal position in place of Surrey. Some of my team (though not the pair directly affected - whose view was "we've asked the TD, he's given his judgement and that should be that") thought we should appeal; I discussed it with Frances & Jeffery amongst others (even though they weren't strictly impartial, but I thought I could trust them) and I was persuaded that an appeal would fail and that I wouldn't waste everyone's time.