"Aren't Linear Regressions of variables with trends always plagued by high r-squared values" is certainly not true. Sure, there are instances of that, but it's definitely a stretch to say that it's always the case.
Two, a high r-squared valued in itself does not necessarily mean spurious correlation. This example of comparing current stock prices to lagged prices certainly does not strike me as spurious. In other words, it definitely does not strike me as belonging in the same category as the classic Wall Street example of skirt lengths being correlated with the direction of the stock market.
Three: RWH proponents nonetheless acknowledge that linear regression might not be the appropriate tool to bolster their theory. Yet other methods offer support to theory as well. Fama, in his paper, states
"These criticisms of common statistical tools have not gone unheeded, however. For
example, Alexander’s filter technique [ 1, 2] is an attempt to apply more sophisticated criteria to the identification of moves...In Alexander’s latest work  it turns out that, even when the higher broker’s commissions incurred under the filter rule are ignored, the filter technique cannot consistently beat the simple policy of buying and holding the indices for the different periods tested."
With that being said, I would not say the RWH perfectly describes the stock market. One can point to countless episodes of where the market was not rational. I think the main point is that your machine learning model or algorithm better be top notch. Don't expect outer-performance by just following a how-to article and whipping up a model in a week.