By your definition of meaningful information, it's not actually clear that a strong lossless compressor wouldn't discover and encode that meaningful information.
For example the presence of a face in an image is presumably meaningful information. From a compression point of view, the presence of a face and it's approximate pose is also information that has a very large impact on lower level feature coding, in that spending say 100 bits to represent the face and it's pose could save 10x as many bits in the lowest levels. Some purely unsupervised learning systems - such as sparse coding for example or RBMs - do tend to find high level features that correspond to objects (meaningful information).
Of course that does not imply that training using UL compression criteria is the best way to recognize any particular features/objects.
By your definition of meaningful information, it's not actually clear that a strong lossless compressor wouldn't discover and encode that meaningful information.
It could, but also it could not. My point is that compression ratio (that is, average log-likelihood of the data under the model) is not a good proxy for "understanding" since it can be optimized to a very large extent without modeling "meaningful" information.
Some of you may already have seen this story, since it's several days old, but MIT Technology Review seems to have the best explanation of what happened: Why and How Baidu Cheated an Artificial Intelligence Test
(In case you didn't know, Baidu is the largest search engine in China, with a market cap of $72B, compared to Google's $370B.)
The problem I see here is that the mainstream AI / machine learning community measures progress mainly by this kind of contest. Researchers are incentivized to use whatever method they can find or invent to gain a few tenths of a percent in some contest, which allows them to claim progress at an AI task and publish a paper. Even as the AI safety / control / Friendliness field gets more attention and funding, it seems easy to foresee a future where mainstream AI researchers continue to ignore such work because it does not contribute to the tenths of a percent that they are seeking but instead can only hinder their efforts. What can be done to change this?