We've been round this rock before. An FI having the 'no applied instrument' restriction removed in order to teach for the IR needs (amongst other things) to have flown 200 hours flight time under IFR and to hold an IR him/herself. Since his/her IR requires 50 hours of IF and that can be counted x4 to equate to 'flight under IFR', 4 x 50 = 200, so hardly a problem.
An IRI is an entirely different qualification to a FI-with-applied-instrument-restriction-removed and is a standalone qualification requiring 800 hours of 'flight under IFR' (400 in aeroplanes) - and that could indeed be totally meaningless VFR navigation exercises.
Unfortunately, lazy FTOs tend to refer to these qualifications as though they're the same thing - 'IRI' being simpler to say! An IRI only teaches instrument flying for the IR(A) or IMC Rating; however, not being a FI, this presumably means that an IRI cannot give instruction to pilots who do not hold licences - e.g. pilots on an integrated CPL/IR course who do not hold PPLs. Incidentally, a ME IRI must also meet the qualifications for ME CRI.