:~/scripts/perl$ mount
/dev/sda1 on / type ext4 (rw,errors=remount-ro)
proc on /proc type proc (rw,noexec,nosuid,nodev)
sysfs on /sys type sysfs (rw,noexec,nosuid,nodev)
none on /sys/fs/cgroup type tmpfs (rw)
none on /sys/fs/fuse/connections type fusectl (rw)
none on /sys/kernel/debug type debugfs (rw)
none on /sys/kernel/security type securityfs (rw)
udev on /dev type devtmpfs (rw,mode=0755)
devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620)
tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755)
none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880)
tmpfs on /run/shm type tmpfs (rw,nosuid,nodev)
none on /run/user type tmpfs (rw,noexec,nosuid,nodev,size=104857600,mo
+de=0755)
none on /sys/fs/pstore type pstore (rw)
systemd on /sys/fs/cgroup/systemd type cgroup (rw,noexec,nosuid,nodev,
+none,name=systemd)
/home/myuser/.Private on /home/myuser type ecryptfs (ecryptfs_check_de
+v_ruid,ecryptfs_cipher=aes,ecryptfs_key_bytes=16,ecryptfs_unlink_sigs
+,ecryptfs_sig=cdf62344e76957d1,ecryptfs_fnek_sig=88d715cd172f27b9)

:~/scripts/perl$ ls -l /home/myuser/scripts/perl/
total 248
-rwxr-xr-x 1 myuser myuser  5962 Jul 10 15:16 flash.pl
-rwxr-xr-x 1 myuser myuser  5962 Jul 10 15:16 flash2.pl
-rwxrwxrwx 1 root root   183 Jul 10 14:54 asdf.pl
drwxrwxr-x 2 myuser myuser 90112 Oct  9 11:04 flash

:~/scripts/perl$ ls -l /usr/bin/perl
-rwxr-xr-x 2 root root 10416 Mar 27  2014 /usr/bin/perl

:~/scripts/perl$ file /home/myuser/scripts/perl/flash.pl
/home/myuser/scripts/perl/flash.pl: Perl script, ASCII text executable
+, with very long lines

:~/scripts/perl$ head /home/myuser/scripts/perl/flash.pl
#!/usr/bin/perl
use warnings;
use strict;
use DateTime;
use LWP::UserAgent;
use Data::Dumper;
use DBI;

#Get yesterdays Date

:~/scripts/perl$ /usr/bin/perl -le 'print "Hello, World"'
Hello, World
[download]

The suggestions were meant to be placed in the crontab, but that doesn't matter anymore, since the problem has been discovered:

/home/myuser/.Private on /home/myuser type ecryptfs (ecryptfs_check_de
+v_ruid,ecryptfs_cipher=aes,ecryptfs_key_bytes=16,ecryptfs_unlink_sigs
+,ecryptfs_sig=cdf62344e76957d1,ecryptfs_fnek_sig=88d715cd172f27b9)
[download]

Yes, the home directory is encrypted, so it is not available when the user isn't logged in. One solution is to drop the scripts in a non-encrypted location (/opt or /usr/local or whatever suits your system) outside of the home directory and it'll work.

$ sudo mkdir /opt/myscripts
$ sudo chown myuser:myuser /opt/myscripts
# put scripts in /opt/myscripts
[download]

Crazy. I never would have guessed that one, I can move the scripts. Thank you all of the help!