I don't think the safety record back then was all that great. Lets look at the stats....

manned flights
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Mercury = 6
Gemini = 10
Apollo = 16 (including Apollo 1, Skylab I, II, III, and ASTP)

That is a total of 32 flights. With 1 fatal accident/destruction of vehicle (Apollo 1).
That gives a failure rate of 3.1%

The space shuttle has had 113 flights and two failures. That's gives a failure rate of 1.8%
I don't think safety was much if any better back then.
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However, the number of missions between failures is slowly increasing (way to slowly.... but flights between accidents is about doubling every time)

Before Apollo 1 = 16 flights
between Apollo 1 and Challenger 51L = 39 flights
Challenger 51L to Columbia 107 = 87 flights