A counterexample to this claim is the experience of families moving internationally. It's always the children who pick up the local language faster.
I would hazard that in those cases, the adults still operate in their own languages as much as they can. The children spend many hours a day in situations where they cannot do so, or where the consequences of language inability are not short-term catastrophic. Schooling, for example. I suspect that in those situations, the adults find ways to continue to operate in their own language, out of necessity; they don't have the luxury of spending several hours a day fumbling their way through basic grammar. Those adults need to work, so they will work where they can continue to use their own language, or at least get by with hand-signals and a hundred words. Often, people moving internationally group together with other immigrants, continuing to operate in their own language and culture. They simply avoid learning.
This certainly does happen. But equally, the adults are often making a much greater conscious effort to learn the local language than the children are, and yet are almost always less successful.
I doubt that it is universally the case that the adults are "less immersed" than the children, but it does seem to be almost universally the case that the children acquire the language faster.
A few hours a week fumbling with a basic grammar guide is certainly better than a few hours a week immersed and desperate to communicate, but fifty hours a week immersed and desperate to communicate is what the children get and that will always do better than a few conscious hours a week with a basic grammar.
When I say "immersed", I don't just mean "surrounded". I mean it's coming at you, deliberately, and it's your only option for communication that you are desperate to engage in, mind spinning and whirring, latching onto constructs and experimenting with them, every human social fibre in your being that demands you communicate and connect with the people around you (and that is a very strong part of being human) driving the desperate urge to learn the fucking language, on the order of 10 to 16 hours a day.
I suspect, however, that for a typical immigrant, the child does not spend their days in a school taught in a non-local language, but instead simply goes to the local school, and I suspect that for a typical immigrant, the adult does not work in a building whose working language is their own native tongue. Your (husband's) experiences are somewhat offbeat.
This is something that I think happens not just with language, but with other traits—personality, skills, etc. A lot of these things can be more mutable than “expected” purely based on what a “self” can withstand, but the expectation itself causes friction and inertia from both directions: the person has to adjust their self-expectations, but also the social environment has to add energy and information to make those changes happen in a way that's integrated with the world. For anything that isn't adequately compartmentalized, sometimes there is no effective framework available; if the people around you already think they know you, either by broad categorization or by previous experience, you have an uphill battle. Children are more socially recognized as mutable, so both adults and child peers are more likely to put in the energy, and they're also placed in roles where experimentation is safe.
Hope that helps :-)
betaby above, an immigrant, suggests this to be the case.
Kids naturally are still developing their worldview and learning how to make relationships thus new culture and language is just an another step in that process.