I think this is quite a broad statement. I would argue that all the games influence each other. Just like writers, musicians, and visual artists, the game designers learn as they go. THey make a game and see what works, what doesn't work, what was liked by the fans and what wasn't, etc, and then build off that new knowledge for the next game. So, did OoT influence TP? Of course it did. Just like WW influenced all the games that came after it, SS will be influenced by OoT, TP, WW, ST, and all the rest as well.
Some of the influences might be more or less apparent to us as players, but they are all there. Using the example of SS, from what we have seen it is going to mix TP and WW's graphics and design with the cel-shading, 3D, older Link. But the story might be similar to PH. We don't know yet, at least we don't really know yet.
On the issue of OoT and TP. I do agree though. I see the similarities you have mentioned, but I don't think they are overly significant. I think the use of the songs was for nostalgia sake, and fan appeasement. With the dungeons, again, I see your comparison, but TP was a dark and gritty game, more so than OoT with a large sense of realism. THough this is largely due to advancement in graphics, I don't think they were meant to mirror each other. But OoT was one of the favorite games of all time, so TP took one portion of that, dungeon appearance and experimented with that. Lots of fans were unhappy with the dark graphics, and now we see the reprocussions of that response with SS.
The dungeons themselves are all very similar throughout the games in terms of their patterns. All video games follow patterns of function and mindset for the player. Most of the time this is dependent on the genre. Most adventure games have the same patterns, as most shooter games have the same patterns. This is why game players fall into liking or disliking one genre over another. Depending on how one individual thinks, it may be easier or more challenging to play a game mentally, based on the game's patterns of function. All the games in the Zelda series are the same genre (obviously, lol) and are are modeled on the same basic patterns. THis makes all the dungeons very similar in playthrough. Some fans like that other do not, they want a new challenge.
And I'm feeling like I'm starting to ramble, so to wrap it up, I would say that yes, TP was influenced by OoT, but it was also influenced by all the other games that came before it.