Jeffrey, there is no such requirement. Someone who marries an American cannot immediately adjust to permanent resident status, but is (typically) granted conditional residence, which is in practice the same thing except that it can be easily revoked if it looks like the marriage is a sham. After 2 years the not-so-newlyweds can (in fact, must) apply to have the conditional status removed, at which point the foreign spouse becomes a permanent resident. This is almost always a formality except in cases of marriage fraud or involvement in criminal activity. There is no requirement to leave the country. In fact, for people who have been married longer than 2 years or living together a long time, USCIS will sometimes waive the conditional status (and thus the fee to have lifted later) because they have prima facie evidence of a bona fide relationship. It's only in cases where they have serious doubts about the honesty of the applicant that they require the couple to leave the US and wait several years to reapply.
IANAL but you are definitely misinformed about this, and should not allow it to interfere with your love life.
IANAL but you are definitely misinformed about this, and should not allow it to interfere with your love life.