And thanks to absence of other activities, her character could show in the garden.
Tatiana's participation in a great many activities is well documented: swimming, kayaking, bicycling, correspondence, photography, sewing & embroidery, charity work, nursing....
IMHO the version about that was an exceptionally good gardener is very probable.
I don't mean to be snarky, but in the absence of a source, this is as probable as saying Tatiana was an exceptionally good cook, or a remarkable clarinetist. With a few exceptions, Romanov fan- and websites are notoriously inaccurate -- and we don't even know the name of the site this supposed information came from. Until we do, Ally is right to treat this anecdote cautiously.
I see it was not Tatiana, but Olga...well, maybe Olga was a bit of a greenthumb herself, or maybe she was just required to do it. Who knows?
In this instance, it was required for the ceremony. If I recall correctly, there's film footage of each of the girls contributing a shovel full of dirt in turn.