If there is a Toyota Technical Service Bulletin that says this is acceptable, it's give or take. Google search Technical Service Bulletins for your car. This would mean Toyota engineers tested that particular engine design with the lightweight oil, deemed the performance and wear to be acceptable, and they told dealers this swap is acceptable. 

In my experience, Ford did this in my 1999 Ranger in 2003, back spec-ing the 3.0L Vulcan to be 5W-20 compatible along with OE 5W-30. I found this out after mixing up my Mustang and truck's oil weights and found it was acceptable. I did not stay on the switch. The engine burned about a half quart more oil over a 5,000 mile oil change interval than the 5W-30. I switched back. Thinner oil than specified in an engine allows it to "leak" more readily past piston rings, etc. and be burned, even if the engine has no such issues on the heavier oil. The oil film of thinner oil is also easier to break down under high loads, thus it can lead to premature engine wear.

If that car has VVT, you don't want to mess with the engine oil weights. The car was designed specifically for the 5W-30 weight, and lighter or heavier oil will screw with the system. Personally, I would switch it back. 5W-30 was what the engineers specified in the beginning, stick with that. 

Search for the technical service bulletin like suggested above. I think your car is in the era where both weights are ok. Older Toyota needs 5W30. Newer need 0W20. Super new need 0W16. But yours is probably in the era where 5W30 and 0W20 were ok for the engine. 

As a cynic, I'll bet the dealer just gave you what they have and didn't care at all what the car really was supposed to have.