You are quite correct but only if you are using an old style non-jaa fuel policy. For many years we used the old CAA policy that required (if I remember correctly) fuel to divert from your destination (missed approach point) and divert to your alternate, hold for 20 minutes (could have been 30) and then make an approach. You could have in theory have held for 20 minutes and landed with nothing and still have been legal. You were also obliged to divert when you got down to alternate + alternate holding fuel rather than, under certain circumstances, ditching the alternate and continuing to hold at your destination using that fuel. In practice of course if you had diverted and were told there was 20 minutes holding you would (should) have declared an emergency and landed anyway. The newer policy just formalises that process and says that you if you expect to land at your destination or alternate with less than 30 minutes holding fuel you MUST declare a mayday.