Sure, somebody could anonymously push a patent-encumbered solution and make it available to the public, but there's a lot that could and would be done to prevent the public from using that solution if the patent owner (or whomever they sold the patent to) wanted. That would just create a "poisoned" version of the software that's taboo for every legitimate user because it opens them up to a cease&desist + requirement to pay fee+penalties for previous use.
For starters, if running a full node required to run patent-encumbered software then (no matter if that software was published on the internet) all the legitimate exchanges would be prohibited to use the software, and any US merchants would be unable to accept bitcoins, since they can't use the software anymore and any USA payment service providers who could handle the transactions for them would also be prohibited to use the software without licensing the patent.