When tuning, for intonation or performance, the guitar should be on the neck pickup and the tone control rolled off to supply the fundamental tone with few harmonics. The harmonics can throw off a tuner.
And, anyone who wants to make themselves crazy, it seems we can use the tuner’s “tuning-fork” mode to send a signal into the modeler and see if they agree on the pitch. Then reverse the order and use the SYNTH block to send a signal to the tuner and see what it says. Finally send the FX3’s SYNTH output from OUT 2 into INPUT 1, and engage the tuner and see if the FX3 agrees with itself. Then meet in a back alley at midnight and be prepared to discuss the results.