I can concur that
John Barrett's Bristol Classic Rums are very good examples of pure rums, with no funny methods used. Tasting such rums, many single cask releases, is an eye-opener in many ways - for example, these rums are very dry in taste, when compared to almost any "mass-market" rums sweetened generously with added sugar. They also showcase aging quite well, and make an interesting comparison to tropic-matured rums claiming to be all 30 years old etc.
Cadenhead's is another brand that has bottled pure rums, as is
Gordon & McPhail. In general, there is a lightyear of difference between the taste of mass-market products, and these independently bottled rums, which often appeal more to Single Malt Whisky drinkers, for the very fact that they haven't been "tampered" with, but also because the taste is often closer in style to whisky because of the lack of tampering.
Richard Seale is doing pioneering work also in Bim (Barbados, that is), and for example the single cask from him bottled for Milroy's of Soho whisky shop in London was amazing & pure. Savana distillerie, and Riviere du Matt from Reunion also produce fine, natural rums for example. I think Rhum Martinique's are generally so regulated, that they are pretty pure.
Finally,
Silvano Samaroli and
Luca Gargano from Italy have absolutely fantastic old Demeraras and Caroni rums for example, all which are bottled at full strength, and without any funny business.
As a footnote, I think most rum lovers, especially those in USA, would be shocked tasting a rum that has not received any "fixes". The dryness would hit as number one issue, and then - well, the richness of natural flavours, not hidden underneath excessive filtering, added fruit, oak extracts and sugars etc. If sweet sugar (or aspartame!) is what you like, you will not like Rum - as it is from the cask, I suspect. And I do believe rum straight from the cask is similar in this sweetness aspect, no matter what the distillery.
Anyways, there's a market for every style, I just wish that companies selling mass-market rums would be more honest in the rum business as to what & how much they add to their products.