Inorganic nitrate from say potassium nitrate does not raise nitrite levels in a well filtered tank. For inorganic sourced nitrate to start having fish issues you are talking in the 1500ppm levels, many many times the levels you should be dosing at. Due to a pump failure I ran with 350ppm nitrate (and 80ppm phosphate) for a week with no fish or plant issues.
However organic sourced nitrate, not that you can tell the difference or test between inorganic sourced and organic sourced, they are the same, nitrate is nitrate, is the smoking gun that indicates something has gone wrong or tank is not cycled. Ammonia from uncycled tank, new substrate, rotting plants, rotting fish is toxic to fish. This then converted to nitrite, which again is toxic to fish before finally being converted to "harmless" nitrate.