No problem, what goes around comes around 🙂
It's not curl or wget specifically that is the problem. It's the idea that you can run a script through "port 80" that's unprotected. Hopefully your remote machine is behind a firewall and port 80 is blocked... or , if it's not blocked.. hopefully you have some way of keeping someone in japan from hitting your PHP script. Perhaps you could put in a .htaccess file in your web directory to only allow 127.0.0.1 (localhost) from hitting that script.
Making conditional executing in a cron process will be a little hard to describe in this forum. What I suggest is putting the commands in a shell script and call the shell script instead from the cron jon... take a look at scripts in any unix host in rc.d like /etc/rc.d or /etc/rc3.d or any of those startup type scripts, they always test for a file or for exit codes. It's just one place to check for sample scripts, you can find them on the net as well.
In short, I'd say, write a shell script that tests for the existence of the copied file, checks to see if the time is up-to-date (for example) then, issue the curl command from the script.
Hope it helps.