If you're more specific in the thread title, you'll find that more people will actually read your post. Also, ask the question up front...then elaborate for those who want additional details.
I mount and unmount tires from both my own and my wife's road bikes without levers every time...and have no problems with blowouts.
On tires that aren't crazy hard to mount (actually with all tires), it's important to check the tire bead all the way around the rim to make sure it's all seated properly during inflation. Even if a tire and rim "fit" properly together, if the bead seat of the tire has collapsed too far into the rim at one or more spots, the tire can be blown off the rim on the opposite side where the tire is has more slack than it should.
The other thing that will cause this type of blowout is having a tube pinched between the tire/rim during installation. At some random point, the tube will blow the tire bead off of the rim.
-Jeremy