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I believe you've just hit a limitation of the OGR SQL engine.

http://gdal.org/ogr/ogr_sql.html mentions :

WHERE Limitations
   1. Fields must all come from the primary table (the one listed in the FROM clause).

There's however a workaround (at least from a programmer point of view...) : instead of issuing the ExecuteSQL() with the where clause included, just issue the ExecuteSQL() with only the join and on the resulting layer, apply a SetAttributeFilter() with the where clause.

Illustration with ogrinfo (>= 1.8.0 --> from the error message you get I see you are using GDAL/OGR < 1.8) :

ogrinfo ../autotest/ogr/data -al -sql "SELECT * FROM poly LEFT JOIN idlink ON poly.eas_id = idlink.eas_id WHERE idlink.name = '_170_'" 

doesn't work (results in a layer with no features),

but :

ogrinfo ../autotest/ogr/data -al -sql "SELECT * FROM poly LEFT JOIN idlink ON poly.eas_id = idlink.eas_id"  -where "idlink.name = '_170_'" 

does

The dark side of this is that applying the where clause as an attribute filter after getting the OGR layer could be less efficient than applying it in the SQL request, in the case the where clause would only refer to fields of the primary table and that an index existed on those fields

The subset string is meant to work on provider level (e.g. on the database to have best speed). It would be a possibility to have a fallback to clientside search string. For the moment, the dialog is just greyed out as soon as there are joins on the layer (commit 3ac604ff1be4676e69e2).