The vast majority of UK rail fares are "settled" between train operating companies (TOCs) through a central system called the Rail Settlement Plan (RSP). When you do a search on National Rail Enquiries you will see RSP fares (some exceptions may include some Open Access Operator fares).
TOCs can discount certain TOC-only Advance fares (i.e. Advance fares that are for routes wholly within their TOC franchise area) in order to attract customers to book directly with them rather than with a third-party retailer like TheTrainline (or another TOC). The TOC still has to pay the full pre-agreed price through RSP, meaning that they will be making a loss on these discounted fares (offsetting the loss as a marketing cost because the customer is likely to book directly with them again in future).
Rather than selling tickets to individual customers, "rail-appointed agents" are usually Travel Management Companies (TMCs) buying tickets on behalf of corporate travellers (see this thread). My understanding is that agents can only issue fares via RSP just like any TOC or online third-party retailer, and do not have access to any special fares.
It is therefore likely that you have discovered some sort of anomaly and it is not actually possible to purchase the fare.
However, if you are able to provide further information about the TOC and the fare in question I will be able to provide a more precise answer. The regulation of fares and the franchising system in general is a mess and there are some odd exceptions to the rules, and so it would be worth providing more detail.
To answer your question about Loco2, if and when we start selling UK rail we would unfortunately be unlikely to be able to offer any special fares, only what is available in RSP (i.e. the prices you see on National Rail or TheTrainline etc). A "rail-appointed travel agent" is an offline agent, whereas as a third-party online retailer (whilst still an "agent") connects its software to the RSP system somehow. Loco2 would count as the latter.