I just bought a ukulele and had the bridge lowered to make playing a little easier.  I tuned the strings and walked up the scale on each string with the tuner to see how close the notes are.  

Almost all the notes are 20 cent above the tuned note.

So I tried this on a Uke that had not been modified and also on two guitars, and got the same result.  It makes me wonder about tuning the guitar or uke to itself.  You would have one string tuned and the others matching 20 cent high.

Why is this and what can be done to true up the sound?

The frets are not sized properly.

Were the pitches correct before lowering the bridge?

I does sound like the frets are misplaced.

If you tried three known good instruments, I would suspect the tuner.

I have three tuners , rack, inline, and  acoustic. They don't always agree perfectly but very close.

If all the frets are off by the same amount, but open is  tuned, then open is wrong.

The bridge is wrong, I assume that each string is not individually adjustable.

I don't know for sure if the uke was bettter before in terms of the strings.  It was in tune at the store, and I had them work the bridge before we ever brought it home.  

It is bothersome that all of the instruments have the same feature.  By the way, some of the strings are correctly tuned on a few notes as you move up the octave.  This is making me think that it's a fret issue like you guys are saying.

I got out another tuner to check.  It doesn't give the cent count, just bars over and under.  It matches the other tuner on the over and in tune notes.

Each string is individually adjusted.  These are all acoustic, so no floating bridges or anything.

I may go back and have the nut lowered on the one and see if that changes anything.  (Was planning on that anyway to make playing a little easier.)

Intonation.. Or maybe with high frets you are bending

You might be on to something.  If I push the string all the way down to the fret board it is 20 cents sharp, and if I push it down just enough to get a clear tone it is pretty much in tune.

I will have to take all my instruments in at some point to have the nut and bridge lowered on them.  Once that is done, I will try to remember to report back on the results.

My '94 strat does this.  It has the original frets on it.  They have been dressed a few times from what I can tell.  My luthier told me that I will need a re-fret soon.

When I dig a little too deep on the fretboard I get similar results to what you are describing even though it is because my frets are too low.

If it were intonation and you lowered the strings then the fretted notes should all be flat since the lower strings aren't being stretched as much when fretted.