Your two interpretations are both grammatically possible and your description of the differences in meaning is absolutely right. Since you came to the right conclusion, the rest of this answer is probably spelling out what you already know, but it might be helpful to someone else with similar problems. After all, we all encounter ambiguous sentences like this every day...
To answer the question directly: No, nothing forces "or other suitable solvent" to apply to either "water" or "hot water". In this case, the rules of evaluation don't bind either pair of items more closely.
Simply reasoning about it, you might say: "If all that mattered was that it was water, they wouldn't have called the water hot."
... the minimum of [ [ hot water ] or other suitable solvent ]
But as you noted, we can hold off on applying "hot" until we've evaluated the next expression, and it can still make sense because solvents can be hot:
...the minimum amount of [ hot [ water or other suitable solvent ] ]
→ ... the minimum amount of hot solvent
So you move on to what you know about the world. According to the above reading, one needs a hot solvent to dissolve the impure solid. Now, based on what you've learned so far about solvents, are they generally more effective if they're hot, or is that only true of water? You might conclude that it's the water that needs to be hot, because many solvents are more effective than water at any temperature...
However, once you consider that the subject is crystallization, you discover that the temperature of the solvent is relevant for this particular application. Of course, the catch-22 is that this is the very subject you're learning about right now, so you're not likely to know this already. So you may have to quickly add to your knowledge of the world with a search result or two.
Even if you stopped there, you probably have enough certainty to proceed on the assumption that "hot solvent" is correct and not "hot water". But luckily this whole limbo of assumption doesn't last long, because you're reading a sentence out of a whole chapter — and context, which is your strongest tool, allows the author to clarify what they mean. As people usually do in life. :)
Edit: That this sort of ambiguity is inherent in all languages and difficult to resolve is demonstrated very well by David Bellos in Is That a Fish in Your Ear?, his book on translation:
An EU regulation exists that allows member states to make exemptions from the general rule for the 'transport of animal carcasses or waste not intended for human consumption'. [A] firm that had been fined in the UK had been transporting animal carcasses to butcher's shops, which clearly intended to sell them for human consumption. But the lorry firm claimed it was exempted from the rule by the EU clause just quoted [...] The lorry firm's lawyers claimed that waste not intended for human consumption and animal carcasses in general (whether intended for human consumption or not) were exempted, where as the UK courts had considered that the exemption only applied to waste and animal carcasses NOT intended for human consumption. [...]
The issue at the heart of this case is a familiar problem in the language of law and in language in general: when you have a list of nouns followed by a qualifying or restricting phrase, where do you put the brackets? Does the restricting phrase restrict every member of the list, or only the last one? Does the expression 'children and women with babes in arms' include children with babes in arms or does it not?
In daily usage we leave disambiguation of this kind to common sense and context.
He goes on to describe how the court examined all 23 versions of the exemption in the different languages of the EU, and found only one (Dutch) where the restriction "not intended for human consumption" unambiguously applied to both "animals" and "waste". This was taken as the authoritative version, and the firm had to pay the fine.
The syntax of this example isn't identical to the one you cited, but it's the same problem at its core. How can you know what a modifier applies to? Apparently you shouldn't ask the European Court of Justice. (Incidentally, I think common sense would have been sufficient if it weren't a legal case: if "not intended for human consumption" only applied to "waste", why would they even mention it? Is there any animal waste that is intended for human consumption? But in law you must be sure!)
By the way, it's worth noting that this kind of ambiguity is quite easy to avoid orally. Your intonation, pause points, and even stress generally give strong hints as to what applies to what. For instance, in @Tᴚoɯɐuo's example about "breast milk (or formula)", the term "breast milk" is a compound noun rather than an adjective + noun and hence must be stressed on the first syllable, which signals to the listener that "breast" cannot apply to "formula".