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Even if you do have a perfectly rectilinear pinhole camera you would still need to calibrate the FOV of the camera for the pose estimates from ar_track_alvar to be correct.
What is the distortion free camera you're using? I may be wrong but I suspect that it may mean that the lens doesn't have any barrel distortion, not that there is no distortion at all. Either way you will still need to calibrate your camera following the instructions shown here and make sure that the correct camera information is being published by your camera node. When you've completed this process you'll be able to find out exactly how distortion free or not your camera is by looking at the values in the calibration file.
The other thing to check is that the size of the markers you're using has been defined correctly, I think ar_track_alvar defaults to 5cm marker size but it can be adjusted in the launch file.
If you calibrate your camera and ensure the marker size is set correctly then the pose detection should be very precise at close range in well exposed images.
Hope this helps.
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