Are torch-on-roofs the best solution for a low pitched roof?
There are many solutions that work well on low slope roofs. There are EPDM membranes and PVC roofs. Those materials are available in large continuos pieces so it's often possible to have a roof without any seams.
I would consult at least two more roofers and see what they say. 
Additionally, did the current roofer locate the problem source? Even though it's often really hard lot find leak sources, he should be able to have an idea of the possible problem areas. It could be that the roof is fine and the water is coming from elsewhere. Proper flashing is extremely important.