There is a lot of gray area between "there are easy, repeatable, provable tests that demonstrate that the randomness this game is severely flawed" and "the shuffler is generating perfect random numbers, string happen even in random numbers, don't be superstitious."
One of my favorite games, Final Fantasy Tactics Advance, has a broken random number generator and I never even remotely suspected a thing on multiple playthroughs. The way the random number generator was modded made it 30% more likely to get a value less than .6 when generating numbers between 0 and 1, or something like that. Very minor, yet definitely a bug. Very difficult to prove. Despite having been played for thousands of manhours like any other A-list videogame, word of mouth and repeated testing didn't expose the RNG to be bugged, it was found to be bugged because some guy who cracked the game's ROM open to examine it noticed it while he was looking at other mechanics people wanted to know about (mostly the hidden stat potential values across various classes).
I'm pretty sure that trust in the person providing a random number is inherent to random number generation. For instance, I could start at the 9,674 digit of pi and produce "random" numbers for your all day, going in order. Those numbers would not be random, yet no test you could devise would predict future digits based on past digits (although there is at least one test I could devise that would predict future digits based on past digits perfectly).
Based on the relative reputations of Square Enix and Making Fun, from my point of view I don't have nearly as much skepticism that it's possible MakingFun is dropping the ball. I do think it's unlikely just because lazy programmers usually copy a very popular RNG implementation, and very popular RNG implementations are usually good, so that's how things usually work out well. But I definitely would not call it "so low it's not even worth the time spent rebutting it", and I wouldn't say that about the Hearthstone shuffler, League of Legends shuffler, or Magic online shuffler either. Generally the best way to know that something is actually and truly random is to see the manner in which the value was obtained : just like in real life, verifying that you see your opponent using proven shuffling methods is a better indicator than looking at outcomes.
Keep in mind that it's not necessarily the core random number generation method itself that is in error, it's also possible that something is done with that value in-between that causes outcomes to tend towards certain values. That's what was happening with the FFTA thing. If there's something not kosher about the way "give me a random number between 1 and 1,000,000" is translated into "give me a deck ordering" then you can get certain orderings to appear more frequently.
I think I will spoiler this post.