Before I express my thoughts on this, I want to let you know that I am a 15 year old with no drivers license nor car, and my only attained technical information is from reading car magazines and scanning the tech sections of various Mustang forums, so even if I do sound like a very knowledgeable and experienced person, please take all of this with a grain of salt if you deem it necessary.
To the best of my limited knowledge, long tube headers significantly increase airflow, so this will result in a leaner air/fuel mixture(less fuel, more air), which is part of why a tune is needed.
Re-adjusting the A/F after installing headers or any airflow increasing modification makes your car run smoother and adds otherwise untapped power.
Also, when long tube headers are added, the catalytic converters are moved downstream from the 02 sensors, causing the PCM to see something out of sort, so it throws a Check Engine Light.
Obviously this is not indicating a problem that could be ultimately detrimental to the engine, but when you get your emissions checked, this CEL won't allow you to pass.
To fix this, people either purchase CEL eliminators(which disguise the CEL) or turn off the 02 sensors(also disguises the CEL). I do not think you can pass with 02 sensors turned off. I am not very keen on this 02 sensor/emissions subject, so it would be best for someone else to elaborate.
Just thought I'd express my information supporting the fact that you need a tune upon the install of longtube headers.
Anyone of a higher level of knowledge who sees any errors in my information, please correct me.