I very much doubt they would lie about it; but if the amount in question was so little that they wouldn't care about it, they would just pay the full price.
Microsoft is composed of people. The people we worry about here, are the ones who might be incentivised to discover exploits before an outsider. They would have an incentive to back-date their work, or their subordinate's work.
They're not stupid. If they cared so much more about pinching every last dollar than about security, they wouldn't have launched the bug bounty program at all.
BTW, as others have mentioned, this is strictly better than the policy of other bug bounties until now, which is "We already found this, so you get nothing"