bash chained logical operator execution order, lazy evaluation

&& and || have equal precedence, so:

When a command passes, it will look for the next && and execute it, even if it is not the directly adjacent operator. You should never use more than one of these operators in a single command list. If more than one is needed you use an if/then construct.

$ true && true || echo yes && echo no
no

This is very much different than:

if true; then 
  true 
else 
  echo yes && echo no
fi

---

$ if true; then true; else echo yes && echo no; fi
$

Or:

$ true && false || echo yes && echo no
yes
no
$ if true; then false; else echo yes && echo no; fi
$

---

I would write your construct as:

if [ -e filename ]; then
    echo filename
elif [ -e ../filename ]; then
    echo ../filename
else
    echo 'ERROR: failed to find "filename"' >&2
    exit -1
fi

I think you are hoping that bash does this:

(A && B) || (C && D) || E

but it actually does this

(A && B || C) && D || E

Where D executes if either B or C succeeds.

Add more grouping:

[ -e filename ] && echo filename || {
    [ -e ../filename ] && echo ../filename || { 
        echo 'ERROR: failed to find "filename"' 1>&2 
        exit -1
    }
}

or

{ [ -e filename ]    && echo filename   ; } || 
{ [ -e ../filename ] && echo ../filename; } || 
{ echo 'ERROR: failed to find "filename"' 1>&2 ;  exit -1; }

or use the very clear and readable if-elif-else style demonstrated by @Jesse_b.

---

Step-by-step, this is happening:

1. filename is in current directory:

   [ -e filename ]    \   # test succeeds, status is now 0
   &&                     # status is zero, will execute this branch
   echo filename      \   # echo succeeds, status is now 0
   ||                     # status is zero, do not execute
   [ -e ../filename ] \   # not executed
   &&                     # status is zero, will execute this branch
   echo ../filename   \   # echo succeeds, status is now 0
   ||                     # status is zero, do not execute
   { echo; exit; }        # not executed
   

2. filename is in parent directory:

   [ -e filename ]    \   # test fails, status is now 1
   &&                     # status is non-zero, do not execute this branch
   echo filename      \   # not executed
   ||                     # status is non-zero, will execute this branch
   [ -e ../filename ] \   # test succeeds, status is now 0
   &&                     # status is zero, will execute this branch
   echo ../filename   \   # echo succeeds, status is now 0
   ||                     # status is zero, do not execute
   { echo; exit; }        # not executed