How does Paul manage to lie so nonchalantly?
Exercise, mostly, I think. Being a public figure implies being exposed all the time, and sometimes lying is the only way to protect your privacy or even safety (while other times it helps mantaining your image and popularity).
But to me another reason is probably that he often tells white lies. Telling white lies isn't technically lying and it doesn't make you feel that guilty nor can get you into trouble, so it's easier to do.
For instance, when he talks about songs that are blatantly about John, I noticed that he tells just the secondary meaning of the song, the general theme. He's not really lying about it, he's just dodging the link to John.
Two examples of this kind of behaviour:
Paul talking about "Lonely Road"
To me it’s not particularly about anything other than not wanting to be brought down. It’s a sort of anti-being brought down song, which is for anyone and everyone. It’s ‘don’t want to get brought down again, don’t want to walk that lonely road’, it’s symbolic for anyone who’s been through any sort of problems. It’s a defiant song against loneliness, written in a hotel room in Goa.
– Paul McCartney, 2001 Paul McCartney – From “The Driving Rain interview” published on paulmccartney.com, November 2001
I hear your music
And it's driving me wild
Familiar rhythmsIn a different style
I hear your music
And it's driving me wild again
Don't want to let you take me down
Don't want to get hurt second time around
Don't want to walk that lonely road again
Paul talking about "This One"
At first he says that the song is "about a relationship" when asked if it is about a marriage, then he talks about how you don't tell people (notice the use of you instead of I in his phrasing) that you love them enough in relationships in general, he talks about Linda, parents; then casually drops the subject of John, but projecting on George, saying that he and John didn't really reconcile. He's avoiding the connection to John as much as possible.
But the song sounds very specific, not so general like it's supposed to be, according to Paul:
What opportunities did we allow to flow by
Feeling like like the timing wasn't quite right?
What kind of magic might have worked if we had stayed calm,
Couldn't I have given you a better life?