Why would he lie about this? What would he achieve from saying that either he or his family missed home? If he was lying and saying "Oh, I was desperate to stay" when he was actually dying to leave I'd understand because that would please us. He didn't. He was honest. He said yeah, it was tough. It got hard for me and the family. I can understand that entirely. Have you ever been away from home for a sustained period? It's hard. Very hard. And, at some point, for many, it just becomes TOO hard.
Are we to believe the people who decided that he wanted to stay and is simply "lying" about it, or the man himself, admitting that the lifestyle in England was too difficult for him to sustain, long term, that he missed his siestas, his culture, his family...missed being able to have something to eat late on when the shops were still open and they're closed, here. It's a completely different lifestyle that he was used to, a much nicer lifestyle than the one we have here. A much nicer climate, too.
Is he lying because his wife was the one that was homesick? It's still true, then, that his family was not settled, if this is the case.
Why is it so hard to believe that he wanted to leave the Utopia of Liverpool to return home to Spain, closer to his family and back in the culture he grew up in?
So, to sum up, he's lying because it doesn't fit with what you believe to be 'the truth'. That's somewhat insecure, don't you think?