No, Private Bodies are not covered under RTI Act 2005.
Bodies termed as "Public Authority” under Section 2 (h) of RTI Act come under the Ambit of the Act.
As per Section 2 (h) Public Authority means any authority or body or institution of Self-government established or constituted -
(a) by or under the Constitution,
(b) by any other law made by Parliament,
(c) by any other law made by State Legislature,
(d) by notification issued or order made by the appropriate Government, and includes any-
(i) body owned, controlled or substantially financed;
(ii) non‑Government Organisation substantially financed, directly or indirectly by funds provided by the appropriate Government.