In episode five, the main characters arrive at a port town where one of them observes European ships in the harbor. He says that he thought European ships were only allowed at Nagasaki. A local man replies that they get away with trading there because they bribe local officials, who then turn around and profit from selling imported European goods in Japan, and that if the bakufu gets wind of it the local officials just claim that the Europeans were shipwrecked in the area.
I know Samurai Champloo is deliberately (and often wildly) anachronistic and makes a lot of things up, but this particular bit sounded plausible to me.
Was it ever known to happen? If it did, surely someone got caught at some point and there's some record of it.
The part where foreign ships were sighted off of the coast of Japan is certainly true, so much so that the bakufu actually passed an ordinance, to fire on western ships that were sighted at the Japanese coast, in 1825, and in 1837 during the Morrison incident, an American merchant ship was sighted in Edo bay and fired upon by Tokugawa forces. The order to fire on foreign ships was later rescinded in 1842. Aizawa Seishisai even wrote about the appearance and nature of foreign vessels something that would have been impossible without some limited contact between Japan and the West, in his New Theses. So the growing idea of a 'foreign threat,' in Japan throughout the 1820s and 1830s was built upon both, more foreign vessels in Japanese waters as well as Russian intrusions in Hakodate.
(Voices of Early Modern Japan. Constantine Nomikos Vaporis.)