Team Sky?
Froome actually tried 2 GTs almost every year
2011: 2nd Vuelta (later changed to 1st)
2012; 2nd TdF 4 Vuelta
2013 1 TdF, no Vuelta
2014: Out of Tour, 2nd Vuelta
2015: 1 Tour, out of Vuelta
2016: 1 Tour, 2 Vuelta
2017: 1 Tour 1 Vuelta
2018: 1 Giro, 3rd Tour
So basically except for the year he won his first Tour he tried to get the Vuelta win every year. Finally got it in 2017, and then what did he do? Go for only one goal? Which would have been the 5th Tour win? No, he tried the Giro-Tour double. Already Froome alone shows how ridiculous the "Sky only cared about the Tour" charge is.
The Giro less successful but tried with Wiggins in 13, Uran then got second, later Porte and Landa were there, crashing out basically.
Of course the Tour has always been Sky's most important goal, as it is for most, now with no Italian teams left probably all, teams aiming for GC in GTs..