Your top 3s of teammates most raced with are now flawed, because their position refer to the number of racedays, not the number of races. Pablo Lastras with 62 shared races is the actual no. 3 on Valverde's list (Purito has 47, wich is also more than Quintana), while GVA tops Gilbert's with 88.
Aaah, ***!
Alright... let me try again. This time without copy-pastying.
Valverde; teammate most raced with:
Imanot Ervit: 122 races
José Joaquin Rojas: 113 races
Pablo Lastras: 62 races
Valverde; rider most raced with:
Joaquim Rodriguez: 128 races
Imanol Erviti: 123 races
Luis León Sanchez: 121 races
Gilbert; teammate most raced with:
Greg Van Avermaet: 88 races
Sandy Casar: 63 races
Mickaël Delage: 58 races
Note that both Christophe Menging and Frédéric Guesdon has also both done 58 races with Gilbert, but fewer racedays.
Gilbert; rider most raced with:
Greg Van Avermaet: 188 races
Sylvain Chavanel: 166 races
Stijn Devolder: 153 races
Pinot; teammate most raced with:
Jeremy Roy: 93 races
Anthony Roux: 80 races
Arthur Vichot: 65 races
Pinot; rider most raced with:
Jeremy Roy: 93 races
Anthony Roux: 80 races
Mikaël Cherel: 78 races
And now, let me compare the "All time teammates" statistics for those three riders.
Valverde; All time teammates (please note that this includes the years during which he was technically suspended):
Imanot Erviti: 18 seasons
Jose Joaquin Rojas: 16 seasons
Andrey Amador/Pablo Lastras: 11 seasons
Gilbert; All time teammates:
Greg Van Avermaet: 7 seasons
Christophe Mengin/Frederic Guesdon/Mickael Delage/Sandy Casar/Jeremy Roy/Benoit Vaugrenard: 6 seasons
And then there are 14 riders he has been teammates with for 5 seasons, not gonna list them all!
Pinot; All time teammates (including this season):
Matthieu Ladagnous: 14 seasons (literally Pinot's entire pro career)
Anthony Roux: 13 seasons
Arnaud Demare: 12 seasons
Probably not that surprising that Erviti and GVA tops the lists for Valverde and Gilbert respectively. Whereas Pinot and Roy were only teammates for 9 seasons, they just did a lot of races together.
Also note that Gilbert - having changed teams slightly more often than both Valverde and Pinot - has no rider he has been teammates with for a decade.