yes it does need to be full fat, basically because the fat helps fill you up.  If the product doesn't contain any added sugar it should be fine.  Some people don't like full fat stuff and that is fine, it does take a while to get used to it especially if you haven't had it for quite some time and others it may not agree with and feel sick after eating something with too much fat. I believe David does mention in his book that as long as it doesn't have any added fat it's your choice to have something low fat.  Take this for example, could you drink 2 cups of full cream milk compared to 2 cups of skim milk, probably not the full cream milk would fill you up more (also providing you like the taste of skim milk lol).

In relation to yoghurt  I don't think it matters whether it is full cream or not. The only significant thing is the sugar content. It is safe up to 4.7% "sugars" because that is milk  sugar [ lactose ] which metabolizes as glucose. A lot of the flavoured yoghurts contain much more. But anything under 7% "sugars" should be OK.

Some yoghurts are loaded with sugar, usually from fruit or added.

I recently had a taste of the Black Swan Greek style breakfast yoghurt, and it WAS delicious.  On the label the ingredients include inulin, which is why it is sweet.  However, in Sweet Poison Quit Plan, David has much to say about inulin, including these words:

"I’m not convinced that we know enough about inulin, wheat dextrin and polydextrose to be certain that their effect on our bodies is not just as bad as pure fructose. I’ll be avoiding foods that contain them and I suggest that all recovering sugarholics do the same."

Pat BAKER wrote:Hi John I totally agree with you about the Black Swan Greek Yoghurt from W/W. I am still to convince my Husband how good it is lol.

If you stop trying to convince him he may come around. He sure won't while he thinks he is being sold a bill of "goods" [aka something which is 'good for' him]  :-)