You are quite right that know in its primary sense has a stative lexical aspect—it expresses an enduring state, without defined beginning or end—while recognize is an achievement verb, with telic, non-durative aspect.
You should be aware, however, that almost any English verb can be ‘recategorized’ to meet the needs of a particular utterance. For instance, as we have discussed elsewhere on ELL, a stative verb may be recategorized as an activity verb by casting it into the progressive mode.
Likewise, stative verbs are often employed with inchoative aspect, in which they express not the existence but the onset of a state. That is the case with your two uses of know: they express the entry into a state of knowing—which happens also to be the meaning of recognize.
For a similar inchoative use of a stative, consider the verb love. Ordinarily we express the inchoative sense of love with the phrase fall in love; but in one of the most famous lines in English poetry (Shakespeare himself quoted it), bare love is used in both stative and inchoative senses:
Whoever loved that loved not at first sight?
Note, too, that the opposite is also true: the achievement verb recognize has a common secondary sense in which it has stative aspect:
The United Nations recognizes the family as the basic unit of society.