In fact the graph proves exactly the opposite. Situations where a user posts only once per month with his alt while being active with the other account are very common, especially if one account is employed by a signature campaign while the other isn't. Usually alt owners like to use their alts from time to time to make it look like the accounts aren't abandoned and/or bump some threads, or back up their own posts. So, that flat blue line with small spikes on it couldn't be more normal for an alt account, it doesn't disprove the claim at all.

Where one person sees something random, another will see a pattern. There are days where both of the accounts are very active, and there are days where only one of them is active, while other is taking a break. It doesn't prove anything. For example, you can posts with both accounts one day, then on the next day see that you got some replies in the thread where you've posted with one of the accounts, log in with that one and continue the discussion, hence on the graph one account gets a spike while the other doesn't.

As for the hours when they were active, it's also hard to read anything as s_therapist is active in both day and night (which to me is crazy, does he ever sleep? Ok, he does, at 10-11 am ).