Try this formula in cell W4:

=IF(V3=V4,INDEX(INDIRECT("I"&MATCH(W3,I:I,0)+1&":I26"),MATCH(V4,INDIRECT("R"&MATCH(W3,I:I,0)+1&":R26"),0)),INDEX($I$2:$I$26,MATCH(V4,$R$2:$R$26,0)))

The calculation determines whether the prior nation received the same score as the current one. In this situation, it looks for the previous nation in the list and changes the search parameters for the score. In this manner, even a perfect tie across the board will result in a list of distinct nations.

Your formula failed to resolve your issue because the INDEX function looks for the first instance of the sought value. If you have already run another INDEX in another cell, it is not taken into account. You will simply eliminate the first occurrence of the value you are searching for (as well as some other values you don't care about) by changing the range to be searched according to the prior result.

Exploding the formula we obtain this:

=IF(V3=V4, 'Checks for a tie
'---------------------------------------------If it's a tie
INDEX( 'Use a index function to pick the result
INDIRECT( 'Use an indirect function to define the range to be searched
"I"& 'State the column of the range to be searched
MATCH(W3,I:I,0)+1& 'Use a match function to find the previous occurence of the score whithin the column of the range to be searched and add 1 to it to cut out that value (and any previous one)
":I26" 'State the closing cell of the range to be searched
),
MATCH( 'Use a match function to determine in what row of the defined range the score is occuring
V4, 'The value to be searched
INDIRECT( 'Use an indirect function to define the range to be searched
"R"& 'State the column of the range to be searched
MATCH(W3,I:I,0)+1& 'Use a match function to find the previous occurence of the score whithin the column of the range to be searched and add 1 to it to cut out that value (and any previous one)
":R26" 'State the closing cell of the range to be searched
),
0 'Specify that you want the the exact occurence
)
),
'---------------------------------------------If it's not a tie
INDEX( 'Use a index function to pick the result
$I$2:$I$26, 'State the range to be searched
MATCH( 'Use a match function to determine in what row of the range the score is occuring
V4, 'The value to be searched
$R$2:$R$26, 'State the range to be searched
0 'Specify that you want the the exact occurence
)
)
)