Except that that window isn't there.That window is just massive and is so open for abuse.
Here's an idea: next time you see a claim like that, a claim that so clearly looks like it's untrue it ought to be waving a flag that says "Bollox!", ask yourself some simple questions.
Like, does it pass the smell test? I mean, if blood can't be drawn before a race/.stage then how were the health checks of the 50% Rule allowed? Or how is the UCI's current pre-race Tramadol test allowed? If blood could only be drawn in the event period after the race then how are the pre-Tour IC tests accommodated? The answer is quite simple: the event period at Grand Tours starts three whole days before the race does. And the rules don't say it has time-outs in which blood cannot be drawn. Or how about considering the night-time tests introduced a few years ago? ("Unless the Rider has identified a sixty (60) minute Testing window between the hours of 11:00 p.m. and 6:00 a.m., or has otherwise consented to Testing during that period, the UCI will not test a Rider during that period unless it has a serious and specific suspicion that the Rider may be engaged in doping.") Don't you think it's easier to draw blood from someone at two o'clock in the morning than wake them up and demand a urine sample, which could take them hours to produce? Be reasonable here.
Then, try asking yourself is the claim supported by the evidence presented, thin and all as it is. WADA's ISTI is easy to find and easy to read. It says that "an Athlete may be required to provide a Sample at any time and at any place". Nowhere in the ISTI does it say that blood cannot be drawn during certain hours.
Just because the ISTI doesn't actually prohibit the drawing of blood before a race does that mean that such a rule doesn't exist elsewhere? In the absence of the rule actually being quoted - which itself tends to be more evidence that you're dealing with bullcrap - try looking at some real evidence. From the 2010 Tour's Independent Observers' report we know that blood was being drawn in the morning before stages. We know that pre-stage blood tests were being carried out at the 2019 Tour. When was the drawing of blood in the morning outlawed? And why? Is Tony Hancock suddenly writing WADA's rules? How much blood do you think is being drawn, a whole arm full?
The people who happily spread misinformation, disinformation and outright lies are one thing and sod all can be done about them. But the people who fall for their bullcrap are something else altogether, they are far more dangerous because they propagate the lies without checking them. And all because they just can't be bothered to look at something and ask: "how could that possibly be true?"