The basement in my house had unfinished drywall on all the concrete
walls when I bought the place. The one thing I noticed was that it
was glued up - I've never really seen that done but I know it's not
that uncommon.

Now, a couple years later I'm thinking of finishing the basement and
taking a closer look at things. I guess I assumed the drywall was
glued to furring strips - WRONG! It appears there's just about an
inch of orange foam insulation (presumably glued to the concrete) and
then the drywall is glued directly to the insulation!

Is this acceptable? It seems pretty iffy to me but the thought of
tearing down 30 sheets of drywall and insulation put up with
ridiculously strong glue makes me feel all woozy inside. Not to
mention I then have to start all over and do it myself.

Somebody save me! Thanks in advance for your help!