I'm not an HFDoc like you are, but with blood clots, you either can play or not play, no? It's not like a physical injury that gets better with rest. I remember that Kreider dealt with blood clots, he had to take time off and go on medication.
You always need to take strong blood thinning medication for at least 3 to 6 months (according to European guidelines, not sure about US but it will definitely be similar), which results in singificantly increased risk of bleeding. That means you can pretty much forget about any contact sports including hockey for that time period.
But there is a huge difference based on where the blood clots are localized. Deep vein thrombosis (i.e. blood clots in the legs) may cause swelling, but in most cases is quite benign (even though blood thinning medication is still a must). On the other hand, if that blood clot gets free and through bloodstream enters into heart and then pulmonary arteries (i.e. pulmonary embolism), it can cause severe problems and (depending on size) even instant death.
I may be a cardiologist in training, but I have no background in sports medicine and no experience with professional athletes getting back to pro sports after this diagnosis, so take it with a grain of salt. But if Andersen had had the latter, I wouldn't be surprised if he still were totally winded doing relatively easy workouts even now, months after. So it seems quite plausible to me that he needs rest.