It's totally not true. Manufacturing fictitious figures like 1800 kg minimum 737 is nonsense. The fact it sets off a Low Fuel Warning is nothing to do with minimum figures- it just makes the digits go a pretty yellow colour. The usual rules are 'Pan' if you are likely to go below minimum reserve which is usually 30 minutes, and 'Mayday' if you are going to go below.
captjns- you show a touching reliance on 'diverting will make it all OK'. In several experiences of diverting, it often ends up being a crisis of its own. Sometimes it's better to hang on to what you have rather than open a door to another houseful of problems!