No, that is not merely conspiracy theorists at work. The Soviets readily admit that the Tu-144 was in fact based around the PRELIMINARY design work done by the Anglo-French, and drawings "obtained" from the French.
If you examine early Concorde design studies, you will note a definite resemblence, even in the wing planform, and engine nacelle arrangement. On the Concorde, after MANY different flying testbeds were flown with different wing plan forms and shapes, they chose the more elegant (and harder to manufacture) ogive delta we all kow so well.
The Russians adapted and adopted one of the earlier wing planform designs, and the earlier nacelle arrangement.
For those interested, I CAN go through all my collection of Air Pictorial magazines from that era to show the progression of the Concorde design - glad I kept them all (probably worth some dosh too!)
Russian designers took a LONG time to finally arrive at significantly independant design styles. Stalin INSISTED that post-war fighters DID NOT embody MANY Me-262 design features - any that DID were doomed to fail, even if they were significantly superior to the opposition. Fighter designers at least seemingly broke the mold of Russian design, whereas the airliner / transport designers liked to imitate...