Yes I'm sure. If I accidently hit the brake pedal getting in the engine would shut off. Cruise control does cancel when hitting brake pedal.
Look in your manual. I looked up mine after I started thinking about it and it does not list hitting the brake as an option for manually shutting off the remote start.
What got me thinking about this again was the other day after work I hit my remote start and got to talking to guys for a few minutes. Grabbed my things and walked out to my truck. I hit the unlock, got in and hit the brake while I was putting the key in the ignition and the truck shut off. I thought, no way, it’s never done this before. Hit remote start again and pushed brake and nothing. Wouldn’t shut off. Thought about it on way home of what would cause that and why I couldn’t repeat it. Until that night getting ready to go to work. Hit remote start and made my coffee. When I went out to truck and got in, it shut off. But that time I didn’t hit the brake. Then it dawned on me, it wasn’t my brake pedal that shut it off, it timed out and was a complete coincidence that it happened exactly at the right time.
I remember a few times when I got in and as soon as I was turning the key the remote start timed out and truck shut off and then came right back on and I thought, what are the chances of that happening more than once. But it has. And I believe that’s what has happened in your situation. The factory remote starts are not cancelled with the brake, only the aftermarket units are. Your manual will confirm this.
Edit: I looked up the manual for a 13 Tahoe. Same thing listed. You just have one heck of an internal clock and your timing was perfect the times it shut off on you.
One way to check this is try your hazards. I’ve never had a vehicle shut off with my hazards that had an aftermarket remote start or the older GM vehicles that had factory remote start. If it shuts off that way then it’s a factory remote start and that’s just the way it is.