A phone is as any computer. If any service on your phone is vulnerable your phone is. You don't need to install an App to get hacked. Vulnerabilities SMS/MMS, the GMS stack and other services are/have been used to infect phone without ppl. noticing.
If need to talk *any thing* sensitive, don't bring your phone.
Some work places even have shielded "boxes" where you put your phone before going in to any meeting.
I have had stuff installed on phone's by "others" without any action hoping I would not "notice".

No, you can not trust your phone is secure.