Is this true that manufacture may change line width when we ask for impedance tuning?! Previously I was thinking that only stack up is subject to change.
Yes, they can do that, but I try to avoid it. Once they start playing with your track geometry or stackup to meet your impedance requirements, you are loosing control over your PCB. This means, there may be differences between your PCBs batches or when you decide to change your PCB manufacturer (the other words, you can get different qualities of PCBs which some of them may behave wierd).
If PCB manufacturer says, that they need to change your track geometry it usually means they can not do your stackup. In this case, if I would like to stick up with the PCB manufacturer I will re-do the track geometry and stackup in our documentation the way it meets their requirements, so they do not have to do any changes in the manufacturing data.