... and don't want anyone to know

Note that there's also ctime, which on most current Unix systems has the semantics "inode change time", and restoring atime is considered an inode change operation. In other words, even though atime could be restored, those who "really want to know" would check ctime in this case...

#!/usr/bin/perl -w
use strict;

sub show_times {
    my ($f, $note) = @_;
    printf "atime=%d, mtime=%d, ctime=%d - %s\n", (stat($f))[8..10], $
+note;
}

my $file = shift or die $!;

# save atime
my ($atime, $mtime) = (stat($file))[8,9];

show_times($file, "initially");

# read from file
{ open my $fh, '<', $file or die $!; <$fh>; }

show_times($file, "after read");

# restore atime
utime($atime, $mtime, $file) or die "utime: $!";

show_times($file, "after atime restored");
[download]

$ touch somefile && sleep 2 && ./fix_accesstime.pl somefile
atime=1386693000, mtime=1386693000, ctime=1386693000 - initially
atime=1386693002, mtime=1386693000, ctime=1386693000 - after read
atime=1386693000, mtime=1386693000, ctime=1386693002 - after atime res
+tored
[download]

Note that even though atime is restored, ctime is still being updated.