Anonymous Monk, thanks for your input. It got me thinking and I created a shell script with a one liner in it:

output=`ssh root@172.17.194.60 /u/remote.script`;
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This also failed, but several print statements in remote.script showed that my back ticked line was not being executed at all! I then created a simple perl one-liner on the remote machine and noted that this worked if I ran it remotely from my shell script.

$result=`/bin/ls -l /u/tns/`;
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Then the answer struck me...my remote.script did not have the full path in front of DB_COMPILE. Once this was inserted everything worked perfectly!

$result1=`/u/DB_COMPILE $from $to`;
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This has been bugging me for ages, so thanks for making me think again and setting me off in the right direction!