That may be the case in India but not in the JAA. The only significant difference between an SFI and TRI is that the former can instruct only on a synthetic training device whilst the latter may also instruct on an aircraft.
JAR-FCL 1.405 - The privileges of the holder of a SFI(A) authorisation are to carry out synthetic flight instruction for type ratings, and the instruction required for multi-crew co-operation (see JAR–FCL 1.261(d)). (It later becomes clear that this is, in fact, limited to MPA type ratings)
JAR-FCL 1.360 - The privileges of the holder of a TRI(MPA) rating are to instruct licence holders for the issue of a MPA type rating, and the instruction required for multi-crew co-operation (see JAR–FCL 1.261(d), Appendix 1 to JAR-FCL 1.261(d) and AMC FCL 1.261(d)).
Details of the requirements are contained in JAR-FCL 1.410 and 1.365 respectively and, although the authorisation must be 'sponsored' by one TRTO, there is normally no problem with freelancing for others. I was a TRI and TRE up until the time I lost my medical and have since been an SFI and SFE. I now freelance for a number of TRTOs, doing as much or as little work as and when I wish.