In these cases, there is no error to abandon, only an additional truth (or additional truths) to discover and embrace. One logical truth going alongside or stemming from another does not automatically mean that an idea is false. Even if part of someone's worldview is incomplete in the strictest sense because there are other aspects or ramifications that a person has not yet recognized, whatever they already knew is not invalid. To know that logical axioms are inherently true does not require that a person knows various other things that ultimately can be proven. The same is the case with other things: knowing some facts does not hinge on knowing all else that is verifiable.
It is impossible to know something that is false, so whatever someone already truly knew as a rationalist would have to indeed be true, but this does not exclude them quickly or gradually coming to rationalistic awareness of any verifiable truth that is not self-evident (aka, that hinges on logical axioms). One could believe what is false and know of the concept in question, but this is not the same as knowing it is true. Anything that is both true by logical necessity (metaphysically) and grasped without assumptions (epistemologically) is still absolutely certain. Nevertheless, where there is more than can be known, a rationalist can grow into knowledge that is more precise rather than more true.
While only things that are true and verifiable can be known, and assumptions cannot be knowledge, not everything that is true is important. While everything depends on logical axioms and is thus in some way connected to them as well as other matters of extreme philosophical significance, there is nothing fundamental or otherwise vital to reality about, say, the fact that dolphins seem to be gray. A rationalist does not have to think of each of these things to know what is absolutely certain and most metaphysically central, nor does he or she have to discover every hyper-precise truth that is important in order to know the core facts of reality like axioms. Acquiring knowledge of things beyond what is self-evident still entails growth over some amount of time. There is nothing to look down on about this on its own.
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