Okay, sure. It's not perfect but it is basically how we conduct ourselves in daily life. And communicating the offer to the other company is part of the general etiquette so they'd be the ones in the wrong if they're put off by it. And as long as the first company doesn't know about this, there's no risk on that side.
It's a business transaction. They know you are interviewing in multiple places. Heck, if you weren't, that means you were not that good. And similarly, you know they talk to multiple candidates