It might be, but it also might not. If you're just cowboy chording, sure, but if you're playing chord melody you'll find the chord you choose is highly contextual based on what you're playing and where you're going. An Am chord is a continuum of notes going up or down the neck A-C-E (G?) over and over-- wherever your hand sits, there's an Am available to you. It just might sound better (or more interesting!) or play easier to grab one set of A-C-E versus another.
I think the parent meant that those voicing are still the same when transposed all over the fretboard. E.g. the first inversion of a V7 has the same shape for all the notes horizontally. To go from A7 to B7, you just move two frets. And if you move vertically, the shape is slightly changed, but still recognizable enough.
A guitar has to be the easiest instrument for transposition (or maybe it's just the one I'm most comfortable with!).
Until you reach the B string. A shape that works on strings 4/5/6 does not work on 1/2/3. This is because G->B is 4 half steps, the rest of the strings are 5 half steps apart. So you need 2 forms for closed chords.
Then you move that note a half-step. The rest is the same. And actually, if you use drop-2 voicing, there are 3 forms because of that half-step, but still the overall shape is pretty much the same. You really need to remember one shape, and then adjust it accordingly.
