Personally, if I'm sick, the last think I want to do is communicate with my manager - it means you have to be careful, you never know if they're digging, or 'professional but not exactly sincere empathy' etc..
'Adult Professionals' shouldn't need to be coddled. If you're sick you're sick and that's that.
If you have something that's a 'big deal' then you have that in a conversation in which the managers emotional response one would expect is empathy but beyond that it's a matter of 'how to work around it'.
'Trust' is a multifaceted thing, I generally do not trust that people will do their jobs well at the outset, until I've seen evidence of that, but as far as those kinds of workplace issues I definitely 'trust by default'. People get sick and that's that.
And then have a lot of tolerance because we are all a little odd in our own ways and it's just easier not to get caught up in stuff.
I trust my manager to not be a dick when I'm sick. I also believe he is an empathetic person who cares about me and wants to know what's up. I understand he has a list of tasks that need to be completed by his small team. So I'm happy to let him know whether I expect to be out for a day or a week.
If I didn't have such a relation with my manager I'd be looking for a job. If he doesn't look out for me when I'm sick he will probably not look out for me professionally either.