Solid states more accurate than tubes?

I assume by true fidelity you mean high fidelity? High fidelity in audio means reproduction of sound without distortion and color that remains true to the original. In order to achieve that you need very accurate measuring equipment. The biggest obstacle now is speakers and room. 

SS is always more accurate.

A digital camera is more accurate than was Ansel Adam's camera and film.

Few would argue the beauty of Adam's work.

I thought the question was which is more accurate in reproducing not creating. The artist   and associatiated technicians creates, we simply try to reproduce what they created. In order to be faithful to that creation then accuracy is paramount. If I don't care for the creation then I can color it with distortion or tone controls that's my decision. But to answer the original question which is more accurate solid state or tubes in reproducing I would say solid state. 

Well, it dependes on what SS and tube amp you are comparing and your personal taste. 

My 300B 805 tube amp (48 wpc) has about 1% THD vs 0.0001% on my Class D amp (400 wpc), both very rewarded among audiophiles. Guess what, I prefer by a WIDE margin the tube amp. Much more real, 3D soundstage, grip, balls, tone and dynamic sound. 

I agree 100% with @jjss49 when he says above "we are painting a watercolour here, not fastidiously documenting an actual event".