Refueling with passengers onboard is quite normal and is done according to the recommendations of regulatory bodies/manufacturers and operators. Refueling with some fuel types are not permitted, while others are. From Airbus Flight Operations Briefing notes:
Refueling with wide cut gasoline type fuel (JET B, JP4 or equivalent) or when a mixture with these types of fuel might occur, is not permitted with passengers boarding, on board or disembarking.
Refueling with Kerosene (JET A, JET A1 JP8, TS1, RT, TH or equivalent, as approved by the approved Aircraft Flight Manual), is allowed when passengers are boarding, on board, or disembarking.
Some precautions are required to be followed in case refueling is done with passengers on board. The announcement you heard is simply following that. From Appendix 1 to JAR-OPS 1.305 Refuelling/defuelling with passengers
embarking, on board or disembarking:
(a) An operator must establish operational procedures for e/defuelling with passengers embarking, on board or disembarking o ensure the following precautions are taken:
(1) One qualified person must remain at a specified location during fuelling operations with passengers n board. This qualified person must be capable of handling emergency procedures concerning fire protection and fire-fighting, handling communications and initiating and directing an evacuation;
(2) A two-way communication shall be established and shall remain available by the aeroplane’s inter-communication system or other suitable means between the ground crew supervising the refuelling and the qualified personnel on board the aeroplane;
(3) Crew, staff and passengers must be warned that re/defuelling will take place;
(4) Fasten eat Belts’ signs must be off;
(5) ‘NO SMOKING’ signs must be on, together with interior lighting to enable emergency exits to be identified;
(6) Passengers must be instructed to unfasten their seat belts and refrain from smoking;
(7) Sufficient qualified personnel must e on board and be prepared for an immediate emergency evacuation;
(8) If the presence of fuel vapour is detected inside the aeroplane, or any other hazard arises during re/defuelling, fuelling must be stopped immediately;
(9) The ground area beneath the exits intended or emergency evacuation and slide deployment areas must be kept clear; and
(10) Provision is made for a safe and rapid evacuation.
You're right about the announcement and leaving seat belt open- it is to help in quick evacuation. The flight crew is just following the procedure.