I don't think there is any truth to these claims at all. Copyright has never gotten in the way of spreading information about scientific discoveries that I know of — it's hard for me to imagine how that would be the case.

Today we tend to see copyright as something that is foisted upon us by big corporate interests (whether that's accurate or not is debatable, but the nature of how intellectual property has been treated and who benefits from it in the USA has changed very dramatically over the last century — see e.g. David Noble, America by Design), but that wasn't why it was created. In the Early Modern period, the lack of intellectual property control meant that worries about being scooped, pirated, and otherwise robbed of one's accomplishments weighed heavily on the minds of several of the major scientists. Galileo in particular took to all manner of complicated secrecy and cipher mechanisms to make sure his priority was preserved, especially when it came to his inventions. (On this, see Mario Biagioli, Galileo's Instruments of Credit: Telescopes, Images, Secrecy.)

Book piracy was rampant in this period and continued through the 19th century. In some sense, sure, it did help "share the information" but it did so at the expense of the author (they didn't get paid for it) and often in the process introduced errors into the works (they were not perfect copies). (On this see Adrian Johns, Piracy: The Intellectual Property Wars from Gutenberg to Gates). Even in the 19th century this was still an issue with regards to foreign republication. Charles Darwin, for example, had no control over who his American publisher would be — it ended up being the first US press to put out a pirated copy, in the end, and Darwin convinced them that they should send him some money each time they sold it in exchange for being able to say they were his authorized distributor. (This is discussed in Janet Browne's Charles Darwin: The Power of Place.)

As for how they varied in country by country — well, they varied a lot, depending on the time period. The history of intellectual property laws is a big, rich, interesting one. But I've never seen anything to imply that intellectual property laws inhibited the spread of scientific information. Rather, the contrary is generally seen as the case: the lack of intellectual property laws led earlier scientists to be very cautious about putting out books and discoveries. To say this is not to imply that copyright today is necessarily this great thing — but it is, perhaps, to push back on the present-day notion, born out of our own IP context, that "uninhibited sharing" is an always positive thing. Scientists in the 17th-19th centuries sure didn't think so.