What a strange notion. Consider:
-RTD confirmed in all the pre-series interviews it was a continuation
-Footage from the old series has actually appeared in the new series. Even audio clip memories (Yana's awakening, among other examples).
-Long-term story arcs are continued, like the Rutan and Sontaran War, the rivaly of the Doctor and the Master, Davros's madness.
-You use the world "similarities" inaccurately. The same actors appear playing the same characters. Sarah Jane explicitly mentions the fourth Doctor dropping her off in the wrong town, and directly references Genesis of the Daleks upon recognition of Davros ("I was there"). This is continuation.
Your logic is shocking. It would be like me arguing that, what if Best of Both Worlds part 1 was in a seperate continuity to Best of Both Worlds part 2? Sure they have the same characters who appear, and the same ship, and same plot, but what if its a bottle universe or something?
Uh....no, it'd be like you arguing that "Classic Trek" isn't in the same universe as "The Motion Picture". Everyone will maintain that they are despite the VAST irreconcilable, stylistic differences between the two. It's like saying that, despite being completely different, that the refit is the same as the original Enterprise.
But people will wink and say "Oh sure, it's the same universe". No....it's sorta the same universe. Ditto for Who. While I enjoy both series, and have an easier time with them being in the same continuity than say "Classic Trek / Post Classic Trek"....they really are just "sorta" the same universe.