I'm afraid I don't have a manpage for ksh. Here's a snippet on here-docs from a bash manpage:

       The format of here-documents is as follows:
 
              <<[-]word
                      here-document
              delimiter
 
       No  parameter  expansion,  command  substitution, pathname
       expansion, or arithmetic expansion is performed  on  word.
       If any characters in word are quoted, the delimiter is the
       result of quote removal on word,  and  the  lines  in  the
       here-document  are  not expanded.  Otherwise, all lines of
       the here-document are subjected  to  parameter  expansion,
       command  substitution,  and  arithmetic expansion.  In the
       latter case, the pair \<newline> is ignored, and \ must be
       used to quote the characters \, $, and `.
[download]

So, if ksh behaves the same way, you can put quotes around PERL and leave off the backslashes:

#!/bin/ksh

USERNAME=`perl <<'PERL'
    use MyUtils::Database qw(ReadResource); 
    my %db_info;
    &ReadResource("$ENV{RCFILE}", 
                  "REPORT", 
                  %db_info); 
    print "$db_info{USERNAME}";
PERL`

echo "USERNAME is $USERNAME"
[download]

That approach works for me in bash.