We have one person's version given to the Media. According to Putin he sat at the same table and Flynn during a dinner with a lot of people present. Putin spoke and left early. He claims he was only made familiar with Flynn when one of his officials told him who Flynn was.
Hearsay is difficult to make judgements on. At the moment the media is simply feeding off one sided titbits, hence there is no real means to evaluate the truth.
The courts, science labs and rational research based on evidence based logic is used by those who base opinions on material matters on weight of or indefeasible evidence.
On the other hand the bottom-feeders of the press who grab at morsels from anonymous sources (such as donkeys' bottoms) pander to the intellectually lame and the mentally crippled.
How is logical relevance defined in the UK?
Here, under the Federal Rules, evidence is logically relevant when it has any tendency to prove or disprove a fact of consequence, or make any fact of consequence more or less probable than it would be without the Evidence. However, even logically relevant evidence may be excluded when its probative value is substantially outweighed by the dangers of unfair prejudice, confusion, misleading the jury, or when its presentation is unnecessarily cumulative. The court balances the probativeness of the logical evidence against its prejudicial effects.
Now, whether evidence is admissible as hearsay depends on whether it falls under an exception or an exclusion, of which there are many. Things like newspaper articles may be judicially noticed (courts take judicial notice of indisputable facts that are either matters of common knowledge in the community or capable of verification by resort to easily accessible sources of unquestionable accuracy), that is, the court may take notice of them and admit them, for example, as evidence of a person's prior consistent or inconsistent statement if presented with them by counsel. The court has wide discretion in this (and many) matters, so it depends once again on relevance and any unduly prejudicial effects, and of course reliability. Once admitted, the evidence can be used to impeach a witness or a defendant provided it doesn't fall into an inadmissible form of character evidence, which is overcome in case where the primary issue involves character (e.g. defamation or in a Trump case, fraud). There's much more to it than that though, really.
The point is, newspaper articles covering statements may or may not be admissible depending on what's in them and who said what. Evidence of this is clear in the fact that the courts who have struck down Trump's travel ban have explicitly taken notice of the language used by Trump and his people who in the past referred to it as a Muslim ban. This is because regardless of the words contained in the writing of a law, if the intent behind the law is discriminatory against a given class of people, the law will be struck down as unconstitutional. In a case of discrimination against national origin, the courts use the highest level of scrutiny, which is known here as "strict scrutiny." Very rarely does anything survive strict scrutiny. The saying is "strict in theory, dead in fact."
So as you can see, public statements posted in the media can be used in court. And really, it's the lawyers who will bring this information to be assessed for its admissibility. That the court can take notice of something is actually almost incidental, but it shows you that statements made in media by certain individuals as well as their conduct, can be admitted into evidence under the appropriate circumstances.
So all this horse-shit railing you're doing against the media is just that: horse-shit. Some of it would be admissible in court, some of it wouldn't. So to deride it all as hogwash is either the result of willful ignorance, or just plain ignorance.