This seems like an interesting idea but it exaggerates things. First of all, I think that everyone thought that there was a large amount of overlap between research being done in the both the US and the USSR (look at the space programs for example). Second, the USSR did do a lot of very good research on their own (look for example how many Nobel and Fields medal they won as a very rough metric).
A quick and dirty estimation: the US shows 331 Nobel Prizes, France shows 58, Germany shows 102; Russia shows 27. Russia is also notably larger than either France or Germany, which it trails badly, and would have been the great majority of people in the Soviet Union.
This table of Fields medal winners shows only 3 for the USSR and 18 for the USA over the period in which the Soviet Union existed.
I think that this belief isn't misplaced. The cost and tech issues seem to be more relevant. Being Daniel Boone in space is really expensive.
The locus here is not "being" but "playing"; "playing Daniel Boone in space" conveys the notion of an unserious, wasteful endeavor. It turns out that people are not actually all that eager to waste those resources for the "thrill of adventure" or "to be pioneers" or the like; yet much of the popular science and science fiction seems to assume this motive, possibly because it was first vigorously marketed to young males at a time when Westerns were a dominant narrative mode.
Asimov wrote an essay for the World Book Encyclopedia in which he laid out what he thought was going to happen.
Asimov was, however, a biochemist and a writer. He wasn't an aerospace engineer or an important physicist; he certainly wasn't someone in a position or with expertise to actually know the feasibility of what he was discussing. In most respects, he was more a member of the media than a member of the sciences; he is certainly more remembered that way, no?
Note that the Nobel prizes are awarded from Sweden, and Russia has traditionally been Sweden's enemy.
SIAI benefactor and VC Peter Thiel has an excellent article at National Review about the stagnating progress of science and technology, which he attributes to poorly-grounded political opposition, widespread scientific illiteracy, and overspecialized, insular scientific fields. He warns that this stagnation will undermine the growth that past policies have relied on.
Noteworthy excerpts (bold added by me):
In relation to concerns expressed here about evaluating scientific field soundness:
Grave indictors:
HT: MarginalRevolution