17" tires on 16" rims and vice versa

[Deborah]

Hi.  I need some opinions.  I have a 2005 Toyota 4Runner.  I also have a 1997 Toyota 4Runner.  Bolt patterns are the same so thats not a problem.
The older truck has 16" rims, with appropriate tires.  The newer truck has 17" rims, with appropriate tires.  
I am considering getting rid of the '05 and getting something else.  
Today I asked the guy at the service desk, as well as one of the service guys, if its possible to put my snow tires that are currently on the 17" rims on the 16" rims?  They said yes, they think so (not 100% sure but they think so).
Also, they said that I can probably put the tires from the 16" rims on my new chrome rims that are 17".
This doesn't make any sense to me.  Don't the tires have to fit the rims?  
My spouse totally disagrees with what Toyota told me today and thinks maybe they didn't understand my questions (but they understood, I'm sure of it).
Thanks!

[tpls]

Tire have to go on the right sized rims.  The service desk person should be fired for telling a customer that.


Tires that are too small will be destroyed by stretching the tire bead over the bigger rim.

Tires that are too big will not seat on the small rim and may will come off.

The shape of the bead of the tire and the inside edge of the wheel rim are very carefully designed and sized so that the tire will stay in place held just by air pressure.