Yes, it is true - though the specifics are, as always, a little more complicated than just saying if you put a 5 ton unit where a 3 ton unit will be, you'll have problems... The reason is http://ianrpubs.unl.edu/generalag/g626.htm . Let me provide a real-world example:
Last summer, a law firm came to my company with a humidity problem: papers curling on desks, copiers jamming - humidity was about 75%. After a study, we found that the basic reason is that the law office has large offices, conference rooms that are often empty, ect. Ie: a highly variable, but generally light load.
The a/c system was constant volume, with two-stages of cooling. (Translation: while they splurged for a widescreen tv and a water-wall in the lobby, they spent more on those than on an engineer to design them a decent system). That means that if the load was light, only one stage of cooling would kick on and the air sent to the offices would be cooled to 65F or so. Now, when an air conditioner cools the air, it cools the air without removing any (much) humidity until the air reaches 100% humidity - then the only way to reduce the temperature is to pull out moisture. So on a humid New Jersey summer day, supplying 65F air means 65F air at 100% humidity. Warm that air up to 75F and the humidity becomes about 70%.
Take a look at the psych chart I linked: On the bottom is dry-bulb temperature. The temp a regular thermometer reads. On the left is wet-bulb temperature. That's literally the temperature measured when you put a wet sock over the bulb of the thermometer. Its the temperature at which water will condense out of the air. From above - at 65F dry and wet bulb (the very left-hand curve, at the intersection of the dry and wet 65F lines), trace horizontally to the right until you hit the vertical line for 75F. That puts you near the 70% humidity curve.
What that means is that with the summer sun coming through the windows, the 65F supply air is warmed up to a room temperature of 75F, resulting in a relative humidity of 70%.
When two stages of cooling are active, the air gets cooled (and de-humidified) down to 55/55. Tracing right from the intersection of the 55/55 lines until you get to 75F gives -- a comfortable 50% humidity.
There are 2 basic solutions: First, and most preferable, simply reduce the quantity of supply-air when you don't need as much cooling. When you do that, the air flows slower through the coil and is cooled more: you get roughly the same amount of cooling with half as much air at a lower temperature. Essentially you changed the way the cooling is being utilized - providing less volume, but more dehumidification.
The second solution is reheat. If you cool the air down to 55F, then immediately reheat it to 75F, you get all the dehumidification without making the space cold. The drawback is obvious: you waste energy through the use of heating coils. However, there is often a way to do this via some sort of heat recovery.
Now, for residential systems, its not as simple as just saying oversizing will result in too much humidity because most are single stage. They do, however, always have multiple fan speeds (sometimes easy to change, sometimes not). If humidity is an issue but capacity is not, slowing down the fan will lower the supply-air temp and improve humidity. They also don't run all the time. So even if they do get the air down to 55F, if they are only on for 5 min out of an hour on a cool but humid spring day, there is only so much dehumidification they can do. Generally, residences have highly variable humidity even with a properly sized system. That said, its guaranteed to be worse if not properly sized.
In offices, air conditioning is used almost year-round. In your home, only in the summer. In the spring, especially, humidity can be a real problem because if its only 75 during the day, people don't run their air conditioning. If its not on, it can't dehumidify. There are some good residential systems out there that can deal with these issues better (Carrier makes a good one), like commercial systems do, but very few people spend the extra $1500 or so for them.
) Very informative, and explains the complex nature of achieving a comfortable environment. I did not know things like how the dew point was different from the wet bulb temperature at anything other than saturation. So now I know you can have cool air that has even greater relative humidity than the warm air if the A/C coil is unable to operate at a low enough temperature to reach the dew point. But now my mind is off wondering how much of an efficiency penalty there would be to have a system that ran the coils at something like 50F on purpose to remove an larger amount of humidity and heat at the same time from the circulated air like in your first solution. 
