Setting aside my bias about whether my large glass of wine last night was one drink or two, I find the claims in this post odd. None of the issues noted seem inherently problematic, and indeed several are as I would expect. Disclaimer: not an epidemiologist, although I do fit models to data and have seen more than a few epidemiology talks.

1: Asymmetric CIs aren't mysterious. Any parameter fit to anything beyond the simplest model and data will have asymmetric CIs. We often neglect this and assume a symmetric (normal) approximation, but in complex data you really should calculate the proper CIs.

2: The data in the age groups wouldn't be expected to be either fully dependent or independent. Looking at the data and assumptions that goes in, some affects all age groups, some only one, and there's model effects between groups (if you die due to alcohol at 30, you can't also die due to alcohol at 50). The CI size lying somewhere between independent and fully correlated is exactly what you'd expect there.

3. The last complaint is a more fair, but also common: most people who die are old, and most causes of death go up when you get old, so CIs get big when you have to subtract large numbers. More data is always welcome there, but also famously hard to get.

So, none of these seem like show stoppers to me, and the way some of them are presented in the post ("mysterious asymmetric CIs") seems to speak to a motivation to knock this study down.

I agree the stats methods in the paper are a bit thin, but I'm not sure how much of that is standard practice in the field. But I think that's a case for asking more detail, rather than denying the results out of hand.