A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
relevant text
Open: if it is not your turn, you have only one province, and you have one or zero cards in your hand: draw a card
if i have one province and it is my opponents turn, i have a full hand (8 cards) does this allow me to draw additional cards?
i would imagine it doesn't (card intent) but the lack of the word only before one or zero means if i have say 8 cards i fulfil the criteria as i do technically have 1 card.
just wanted this confirmed
relevant text
Open: if it is not your turn, you have only one province, and you have one or zero cards in your hand: draw a card
if i have one province and it is my opponents turn, i have a full hand (8 cards) does this allow me to draw additional cards?
i would imagine it doesn't (card intent) but the lack of the word only before one or zero means if i have say 8 cards i fulfil the criteria as i do technically have 1 card.
just wanted this confirmed
You're correct. Having more than one card would make you ineligible to fulfill the requirements of Family Keep's action.
One has to consider that if a portion of card text is meaningless from a purely technical read (because you'd always have one or zero cards in your hand), then what's called for is another interpretation.
EDIT: Also, the Rules actually shore up this problem, above and beyond common sense:
http://rules.l5r.com/CE_Special_wording_rules#Numbers_of_things (emphasis mine): "If the presence of an exact number of things is being checked for, this will be noted by language such as 'exactly two' or 'only one,' or by mentioning two or more specific numbers such as 'zero or one.'"