Can a 800Mhz memory stick be used in a 400Mhz slot?

I have a 3 years old ThinkCentre (A52, type 8381). It has 1GB of RAM in 4 256MB sticks. According to the model spec, it supports 400Mhz DDR2 memory. I would like to increase the amount of RAM I have, given how cheap 1-2GB sticks are today. However, someone told me faster memory sticks (say 800Mhz) cannot be used when only 400Mhz are supported. This is a bummer, because for some reason 1GB of 400Mhz DDR2 costs about 3-4 times more than a modern DDR2 stick with the same size. Is this really the case? Can't a memory stick work in a frequency lower than its optimal?

The best way to check for compatible memory options is with Crucial's tool -- CrucialScan.exe

The Crucial System Scanner automatically analyzes your computer memory information and suggests an upgrade that's guaranteed compatible.

It has helped me on multiple old machines (workstations and laptops).
It will also answer your question accurately for your system motherboard capabilities.

For DDR2 PC2-xxxx and the MHz figures look at this DDR2 wikipedia page.

The two things are similar ways to measure almost the same thing.
Look at the Wikipedia table and small print under it.
PC2-5300 ~ 667Mtps ~ 333MHz and,
PC2-6400 ~ 800Mtps ~ 400MHz.
For normal things, either would not make too much of a difference.
If you get a price advantage, PC2-5300 would be fine.

Here is page-2 of a long article on Dual Channel memory discussing these details.

Further on your comments, people quote frequencies differently at times (probably to make life more confusing for the buyer).
There are a lot of other references that explain these terms.
Here is one more link which has these relevant lines after the explanation.

ddr2 400 = 100mhz internal speed = 200mhz external speed = 400mhz DDR = pc2-3200
ddr2 533 = 133mhz internal speed = 266mhz external speed = 533mhz DDR = pc2-4200
ddr2 667 = 166mhz internal speed = 333mhz external speed = 667mhz DDR = pc2-5300
ddr2 800 = 200mhz internal speed = 400mhz external speed = 800mhz DDR = pc2-6400

The specs on the system you provided shows that you CAN put in PC2 6400 (or 800MHz) RAM. The front-side bus on it supports 800MHz. Therefore, you are able to install the newer type of RAM.

Just because Lenovo cheaped out on the initial build, doesn't mean that the board itself doesn't support the faster RAM speeds.

Go and install away!

-JFV