Actually, no they couldn't. Patents only apply to the right of "first sale". You can resell any patented invention without the consent of the patent holder.
I think you're confusing the first-sale doctrine with exhaustion doctrine, and the latter is, I think, a bit more confusing and unclear as to what patent holders can require.
Secondly, I do follow the sorts of IP law cases that tend to show up on HN as an interested non-legal observer because I think IP law is one of the most dangerous problems the US tech industry faces, even though the industry is the thing that is fucking itself most of the time.
However, from what I understand while the exhaustion doctrine has been upheld for international copyright law recently by the Supreme Court, the same court refused to hear a vaguely similar case as applied to patent law (and the defendant was on the ropes and forced to settle). So there are still quite a lot of open questions about exhaustion doctrine as it applies to patents, especially when international trade is introduced, and also when the original supplier preemptively imposes restrictions (such as the "not for resale" that would certainly be on the packaging of any chemicals sold today). One mitigating thing that might help in this situation though is that price-fixing is often viewed as a situation where such resale restrictions can be found to be invalid.
So, basically this is all really muddy and not entirely decided (exhaustion doctrine is just common law to begin with) and there's no yes/no answer as to whether my half-sarcastic statement is valid, but we do live in a world that is very different than the early 1900s in a lot of ways, many of them for the better, but some of them for the worse.