The scenario is that Full Backups are the anchor for begining a point in time restore. Then you can use DIFF or TRN backups to get recovery faster.
If you restore a Full then you can restore a Diff and then Transaction backups after the time of the diff up to STOPAT='some date and time'.
If the database fails 30 minutes after the backups, you may or may not have the chance to backup the "tail" of the log and recover to that point in time. If it is completely defunct, then you will have to your last transaction log backup. You cannot do point in time with Full or Diff, just with the combination of the Full, Diff and Transaction. If you are missing the transaction log backup then you will not be able to recover point in time.
But one thing to remember about the transaction log backups, is it may happen that you will not be able to backup the tail, but with todays databases, you should be able to. But let's say that you cannot, you should plan your transaction log backups such that you have the tolerance of loss of data. If you cannot stand to lose 15 minutes of data (for whatever reason) then you should plan for that by increasing the frequency of TRN backups.