And yes. It is a problem. If your upstream does skulduggerous things, you can't "route around it" from the standpoint of being an endpoint. Your packets will go where your ISP says they go.
Unless...
You take a bit of the routing decision out of their hands, which takes a bit of footwork on your part. For instance, setting up a VPN to a network zone unpolluted by the faulty prefix announcement, which is basically going to be any non downstream of the hostile ISP provider.
Once you're out of that routing zone, normal network visibility is restored. Odds are even a national scale backbone provider is not going to be able to effectively block traffic that's routing out to a proxy, so all the the ISP has really done is made life more difficult for people unaware of how to set up such an arrangement.
Which now that you know about this, it is your duty to spread the knowledge of how to do so far and wide. If someone wants to block it, then that's all the justification needed for frustrating those efforts.