I realise this is an ancient thread but for any future searches: Might seem a bit left field - ages ago we were having the exact same symptom as OP when trying to add personal Gmail accounts to managed devices... Wouldn't work when on our corporate network - turned out when adding a gmail account to the native app, the device was trying to get out to Google on ports 993 and 5228, which had been disallowed on our firewall. Dropped the phones off the WiFi, and tried on cellular, and it worked fine. Step one, check the network/firewall... :). Hope this helps someone one day!
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