My husband would and does. He's not gay or bi. I know this, because if he were, he'd certainly not be with me but happily married to his gay best friend.
But you would not see the gay couples we are friends with holding hands, or even standing close together if they/we go out. Because it would be romantic for them and they are worried about homophobia, the straight men who have never had to deal with it in the same way, and who don't have to live knowing there are people in the world who would murder them for their sexuality, are the ones who hold hands and are kissy/cuddly with other males in public (especially when drunk). At least in our group.
They just aren't worried about being seen as possibly gay. -- That might sound odd for straight men in the UK, but they don't see being gay as anything to be ashamed of and they don't have the same fear as actual gay or bi friends do.
But they/we are young-ish and in an LGBT heavy friendship group (I'm bi myself, and such).
If your husband is over 35 and isn't super chill about LGBT stuff I think that its something I'd be more concerned about. I think for certain pockets of younger people (especially in LGBT friendly groups), it's normal, though. In fact, it's sort of expected the straight ones in the group will be in some way gender stereotype non-conforming, because that's part of where the affinity and sympathy, and sense of a deep shared belonging often comes from (Bob the macho man, typical bloke, is far less a likely close companion to a gay man who likes to say yas queen and put on my jewellery, even if said gay man is also a broad shouldered chap who is great with DIY and cars). Some of us might not have had it great with our families and the friends become more like family, as well. So, it can be a lot more caring and intense in these groups, and gender norms aren't as much a thing, and being together it encourages that more.
I think also, if he's questioned he's bi...he might have found he's really not into guys at all, but wants to be affectionate with them and that's frowned on and so he thought maybe he was bi. But he's not, ergo to him holding hands with other men is not essentially or exclusively a gay/bi thing. He doesn't want to sleep with them. He likes women, but he is gender non-conforming for a straight man.
So, it could be exactly as he says...but also, yeah he could be gay.