I would never trust any private health data to an app. I don't care what promises or claims they make. The technology is fundamentally untrustable, and even if a vendor is doing the right thing today, they (or any intermediary) could change tomorrow.
Adding to this, my understanding (IANAL) is that any promises to delete or limit sharing of your data could be swept-aside by a bankruptcy judge, putting priority on liquidating the company and its assets for the maximum amount of money for creditors.
If well-intentioned operators erase your data before the company falls into the hands of the trustee or creditors, an unsympathetic legal-system could end up charging them with crimes for it.