The secret is if she can't even talk to him about it now, what is that going to breed in her marriage (if she is in fact planning to marry him at some point). It's a trust issue more than anything. Trying to 'play' games to get him there really isn't being fully honest imho. Play the games, sure but do it with communication and honesty of where you are hoping to go with him.
You may love a person but if you're afraid he's going to not like you and leave by talking to him about this, you don't trust him or the love between you which is common in vanilla relationships.
I'm with stripedangel on this, if she can't bring herself to openly talk about this with him, she either doesn't trust his love for her enough or her love for him.
There is merit in going slowly in this type of communication but truly, if this is a tendancy she has, it's better she learns it now and not three kids and a divorce after 10 years when it finally does manifest itself within her - been there, done that - if it's a real thing inside, it will want release, sometime and will find that release regardless and not always in the healthiest of ways.
She's young and now is the time to sort it out before they both make decisions based on half-truths that will most certainly hurt them later and others around them.
A side note silver hun - I get the whole strict family thing and am not belittling it but at some point luv, you will find your life is your own and if you live it only to please them, you are not making yourself happy and will only resent them in the end for it, losing all respect and possibly love for them. Respect them now by living your life to make YOU happy, not them (of course I'm saying this without knowing how old you are and if you are a minor, then they rule lol).