Middlesbrough has always been in Cleveland - but Cleveland was just the name of the area rather than a county - it then became a county in the 70's but that was dissolved in 1996 - Middlesborough officially became part of North Yorkshire again and still is.
However the border between Yorkshire and Durham is the River Tees - so the town actually straddles both counties.
The Riverside is just south of the river, so replaced The Lane as the closest Yorkshire league ground to another county in 96 and 'Boro can rightfully claim to play in Yorkshire.
My answer remains 'fuck 'em' though.