If you look at the manpage for bash, it specifically mentions this:

In particular The shell does not exit if the command that fails is part of [...] any command executed in a && or || list except the command following the final && or || [...]

This behaviour is exactly as documented/intended.

You can see this for yourself if you run something like this:

#!/bin/bash

set -ex
# set -x will tell you exactly where the shell exits.

_func() { 
  cat non-existant-file
  return 0
}

#_func || echo "Not seen since _func returned zero"
cat non-existant-file || _func
_func
echo "Not seen since _func returned non-zero"

From the manpage:

    set   -e      Exit immediately if a pipeline (which may consist  of  a
                  single  simple  command),  a list, or a compound command
                  (see SHELL GRAMMAR above),  exits with a  non-zero  sta‐
                  tus.   The shell does not exit if the command that fails
                  is part of the  command  list  immediately  following  a
                  while  or  until keyword, part of the test following the
                  if or elif reserved words, part of any command  executed
                  in  a  &&  or  ||  list except the command following the
                  final && or ||, any command in a pipeline but the  last,
                  or  if the command's return value is being inverted with
                  !.  If a compound command other than a subshell  returns
                  a  non-zero status because a command failed while -e was
                  being ignored, the shell does not exit.  A trap on  ERR,
                  if set, is executed before the shell exits.  This option
                  applies to the shell environment and each subshell envi‐
                  ronment  separately  (see  COMMAND EXECUTION ENVIRONMENT
                  above), and may cause subshells to exit before executing
                  all the commands in the subshell.

Which is exactly the case you have here.