Going by what we saw in the manga. If Nagato's abilities are Rinnegan specific, there's no reason for Obito not to use them by himself or through his paths like Nagato does. Obito has not demonstrated being able to use Shinra Tensei, CT, animal summons, etc. But at the same time, if they are specific to the corpses, how was Nagato using all those abilities that his corpses had and how did Madara use Preta Path's ability?
The manga does not prove either Rinnegan or user specificity IMO.
You do realise that the body which was used as Chikushōdō (animal path) was changed by Nagato after Jiraiya had destroyed it, right [
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]? Are you saying that both of these random bodies possessed the ability to summon? This is, of course, disregarding the fact that Madara stated he would teach Obito the jutsu of the 6 paths - these being
specific abilities afforded to those who wield the Rinnegan [
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]. Are you saying that Madara taught Obito how to use Rōshi's Yōton (Lava Release)? It's clear that the abilities are merely specific to the user since, as you say, Nagato used all the abilities in his own body once he was revived. Gedō (Outer Path) is what allows a Rinnegan user to control bodies and, ultimately, project their powers through each realm. Obito was only using one Rinnegan; we don't know if this limits the wielder's capabilities. It's not surprising that Obit's paths had unique abilities because he was using Edo Jinchūrikis as his proxy; Nagato was only (as far as we know) using 'normal' shinobi who lacked spectacular or unique powers. But merely saying Obito cannot do so simply because he did not show to (and then, using this as evidence to suggest that the abilities are unique to the dead bodies) is really silly to be honest.
