Grogs can only gain access to Martial Abilities in a limited number of ways. In fact only three!
Custos is flexible, giving either Martial, Academic, or Arcane Abilities. It gives access to latin as well, plus it gives some special position or status within the covenant, but with no game mechanical benefits. Minor, Social Status Virtue.
Warrior gives access to Martial abilities, plus bonus experience for these. Minor, General Virtue. So, with this you still need a Social Status, but Covenfolk is Free after all.
Privileged Upbringing, gives a lump og exp to be spent on General, Martial, or Academic. By using 'or' and not 'and' one could assume it is only 1 of the 3, not all types. Plus it does not allow buying Martial or Academic with other exp, unless you have another Virtue allowing it. So this option is limited.
You could choose Outlaw (Major Social Status Flaw), theoretically. Although ArM page 17 states that Grogs should not have Major Virtues or Flaws, even if the box in page 37 does not say so.
Outlaw Leader (Minor, Social Status Flaw) is specifically prohibited to Grogs.
So, assuming you want to either create an upstanding, trusted Grog or a combat veteran - or simply ignore the words or intentions of certain rules - you're ok.
But Turb Trained allows some other design. A design that does not have Warrior like most other Grogs may have. Should it have been Free? No, even though it is weak compared to Warrior, by substituting extra exp for Martial Abilities for mere access to Latin, it gives too much to simply be Free. A Free Virtue giving access to Martial Abilities would have been a poor design choice. With the level of granularity available all V&Fs can't be totally fair and balanced to cost.
A new option seems in place