Hmmm...  my response ain't gonna help you - that just sounds baffling.   I was only really adding to / agreeing with @fiddle chick's fine analyses, that I've observed what she says.  

I also had similar/related type problems on the G when I started out - my beginner's "death-grip" on the neck made it difficult to land the finger where wanted without the finger actually "stretching out automatically" - so I was going sharp on each note on the G.  I know that's not your problem - as I say just adding to comment above.

If the fingerboard is WAY out, it might be noticeable - but - at only one tone-step from the open, I would doubt it - the difference would be marginal - it may make a much more observable difference when playing MUCH further up the neck as the clearance from string to fingerboard increases, depending on whether you're "aiming for the string or aiming for the fingerboard" so to speak....

The Snark is in use here as well, just for the open string tuning - I've never used it to "tell me what note I'm playing" ( LOL, maybe I should !!!!! )

Silly question - you say "much lower" - interesting that that is the only sharpened note - does the app clearly differentiate between F and F#  - because "much lower" (like "half way to where you would expect it" ) would be F, not F#...  very strange though.... (yes, I said it was a silly question, but, you never know...)

I know, not much help there - keep us advised on your findings though - I find it hard to believe that there is something fundamentally wrong with your violin !