Thanks Turnbull, I noticed his left-handed handshake too and this leads me to believe that Tessio's treachery began at this meeting and not during the time of/after Vito's death. The theory that 'Tessio as as loyal to Vito as Clemenza was' is something I just cannot accept - I think its clear that he had already entertained the idea of betraying the Corleones before Vito's passing.
However, I think the posts in this thread have definately negated my original query of wether or not Tessio began his betrayal much earlier(during the Sollozo saga) - like I said, it wasn't much of a question in my head as Tessio provided invaluable advice on how to kill Sollozo and Mcluskey but its good to have a logical answer provided for my questions regarding the hospital scene. Thanks very much!