Vincent J. van Heuven holds the position of emeritus professor of Experimental Linguistics at the Leiden University Centre for Linguistics, in the Netherlands. He also studies Experimental Phonetics. This paper, co-authored with Tang Chaoju of Chongqing Jiaotong University, was first published online at ScienceDirect in 2008. It can also be found at http://www.researchgate.net/publication/222820717_Mutual_intelligibility_of_Chinese_dialects_experimentally_tested.
The authors aim "to determine the degree of mutual intelligibility between pairs of Chinese varieties through experiments." They use two types of tests: opinion tests and functional tests. The results showed that the "mean percentage correctly translated target words" was lowest or one of the lowest for the Wenzhou dialect. If those differences are significant, this would seem to corroborate the claim of the Baidu Baike article that Wenzhounese is very difficult to understand.
Eventually, the authors conclude that functional tests work better than opinion tests for making a "family tree" of Chinese dialects. In addition, among functional tests, the tree built on "sentence-intelligibility scores" is better than that of "word-intelligibility."
I shall quote a passage on mutual intelligibility of dialects here:
"Varieties within the Mandarin branch are often claimed to be intelligible to each other to some extent, but are not mutually intelligible to varieties in the Southern branch (despite the recent influence of Standard Mandarin). Most varieties in the Southern branch are mutually unintelligible either to each other or to the Mandarin varieties.... Generally, mutual intelligibility is held to be much poorer for varieties within the Southern branch than between those within the Mandarin branch. Many reasons may explain the mutual (un)intelligibility between Chinese varieties. For instance, the northern part of China is situated on the plains, affording easy travel, whilst the Southern part is very mountainous and difficult to travel through. Accordingly, there may have been less language contact between Southern varieties, which circumstance does not foster mutual intelligibility."
This explanation of the cause of mutual unintelligibility among southern dialects is consistent with my other sources - Baidu Baike, Shen, and my grandfather.