ATC are a member of our team. We need to work together and fully understand one another. They tell me what to do and if it's OK I'll comply. If I need their help, as in a low fuel case, I'd prefer to be specific. Minimum Fuel: Low Fuel: that means nothing to me, even as a pilot unless I know the type of a/c and where it's intended ALTN is. ATC would be even more in the dark. They need specific information so as to make a plan and be helpful. (I used to hate it in the sim when guys with a problem asked for a 'long finals'. Just say 8nm or 10nm or 12nm. ATC have no idea.)
If I would be approaching an airfield with not a lot to spare, as has happened once and there was a queue for snow clearing, I told ATC I needed to be on approach with X mins or I was gone. They then had the information to sequence me. If they needed the same information from other a/c they only had to ask. Min Fuel & Low Fuel is too grey for me. Declaring a Fuel Emergency also has its consequences. It is likely you'll get ASAP treatment and direct as possible, but there will be an investigation and I can understand some being reluctant. However, the old adage of "it's better to be on the ground wishing you were in the air, than being in the air wishing you were on the ground". + "If there's doubt then there is no doubt." Make the call and argue the toss afterwards.