NO....Both LPTA and Stallion are designed and developed by TATA and AL. VFJ basically producing them under license. Both of the products will be marketed by Tata and Al. Basically GoI made them to share the manufacturing with VFJ for unknown reasons since both of them can add additional lines for orders easily due to their scale of operations.
Both are designed by AL and TATA respectively and you are correct till that extent. BUT..... Stallion right is reserved by erstwhile OFB whereas TATA LPTA 715 and 713 right has been with TATA. AL has been involved in manufacturing of Shaktiman series too which again were being assembled by OFB.
Since private companies were not allowed to foray into defence sector, Hinduja group started working in background by supplying kits of 4x4 vehicles to OFB. Only now they are manufacturing them independently with latest being 4x4 Mk IV. You would not see the existing 4x4 anywhere in their offered brochure.
So point here being, AL is involved in defense sector indirectly from even before TATA, but till date they were unable to provide an engine to match TATRA. So, whether DPSU or Pvt, both are same. Only excuse private company could give is that they are new comers in defense sector. But as we could see, that's not the case.