Any new instructor should have been taught the privileges of the rating.
Indeed. The essence of what I currently understand is as alphaadrian describes. But the wording of the passages regarding restricted privileges in JAR-FCL and in the ANO are very similar and quite specific. They refer to two types of training only: initial PPL training, and night training. Therefore if, as you say, a restricted FI can conduct other types of training (continuation training, revalidation training), the implication is that this training could be conducted without a supervising FI.
The reason for the question is that I have been asked act as instructor for a dual hour required for a SEP revalidation in a private aircraft. From a licensing perspective I was fairly confident that I couldn't help them due to being restricted, but after re-reading the JAR–FCL 1.325 passage I'm not so sure.