Hard to answer this. The straight answer is you will need to switch hosting providers. Your hosting provider is locking your blog from communicating out, thus not allowing pings, trackbacks, and many other server to server communications including PowerPress Blubrry Services integration.
Web Hosting Security is a mixture of decisions that each administrator has to make in order to feel satisfied their servers are secured and as free as possible from being hacked. It just so happens that the hosting provider you are using has an opinion that any application you install that can communicate outside of the web server is dangerous and is disabled (disabling allow_url_fopen enabled or the PHP-cURL).
Some web hosting services protect their services by disabling only allow_url_fopen but allowing cURL. Others still claim to protect their servers while allowing both allow_url_fopen and cURL. So your web hosting is not necessarily full of any BS, but you will get a different answer from different web hosting providers as to what they consider secure. Does this make sense?
As far as my personal opinion, cURL is reasonably safe and enabling allow_url_fopen may or may not be depending on how easy it is to install applications on the particular server. If anything can easily be installed and people I don't trust 100% can install them, then I would be reluctant to configure allow_url_fopen enabled. If it is a server that I feel comfortable with the other users/administrators accessing it to installing applications, then I would be comfortable with both allow_url_fopen and cURL enabled. Again, this is my personal opinion, any other administrator is going to give you varying answers.