Rather the contrary.

Pixel density

Of course, as you say, sometimes there is an issue with the sensor - but not directly related with 'more megapixels', but related with the actual pixel density (ie. number of pixels/sensor area). I don't know exactly any more which is the situation right now but it seems that 24 MP APS-C sensors have the biggest pixel density on the market. By tradition, the crop sensors had/have more density than FF ones.

However, the 'pixel density thing' matters when you need 100% (or closer to this) crops. If you want to print at the same size from different sensors then you'll get the same amount of blur, taking in consideration that the 'pixel density' is the only difference between the two systems.

Depth of Field

There are enough places which explain why Depth of Field in the same situation for a FF camera is shallower, and hence you must be more careful to focus (rather than to camera shake) to avoid blur - but take in account that, while this sustain your assertion, this factor can be easily surpassed by the next one.

Shutter speed

The "rule of thumb" for Full Frame is to have the "shutter speed should be at least equal to focal length". That is the minimum shutter speed for a sharp handheld image. So if you have a 400mm lens on the camera then you should shoot no slower than 1/400 sec to get a sharp image.

1. This rule is normalized to FF 35mm. So if you use a 1.6x crop camera (Canon EF-S), you should multiply 1/f times 1.6. In the above example, it would be 1/400 * 1.6, equaling 1/640th sec. * 1.5 for Nikon DX. * 2 for four/thirds. etc.

2. This is an old school rule, back when "sharp" meant an 4x6" print that wasn't too blurred. This is way sloppier than modern day view-at-100% pixel peeping standards. (So use an even faster shutter speed if you want the image to be sharp at 100%.) And scale up (faster) if your camera has lots of megapixels.

3. But contrariwise, the 1/f rule dates from before image stabilization. So you can cut yourself some slack if your camera/lens has image stabilization. (Each "stop" of IS improvement allows for a doubling of shutter speed.)

Hence, this rule of thumb is kind of slip-slidey. But it does give you a place to start from and in practice (I have a little experience with this) FF is more forgiving than a crop one.