Nope, sorry, OP is right. Your justification seems to be that OP's brother's usage was a time-based usage, as in the example in your link. But that simply isn't the case.

The example for a time-based sentence is "we can afford the extra hour". The object of the verb is "the extra hour", i.e. the time being referenced. OP's brother, on the other hand, said that he doesn't "have time to afford it". The object is "it", i.e. the turtle tank, i.e. not a time period at all.

When using the word "afford" in the non-currency sense, it basically almost always takes either a measurable quantity as a direct object, or an infinitive as a complement. The two example sentence in your link demonstrate both of those uses.

I cannot think of any sentence using "afford" in that sense with a concrete object without it seeming unnatural and stilted. Any native English speaker would interpret "afford" with a concrete object as referring to currency or some other direct resource cost. If you examine actual usage, it simply doesn't work for indirect resource costs like time.

So essentially, your summary is backwards. OP isn't claiming that the usage is incorrect because it sounds unusual. But the reason it does sound unusual is because it's incorrect.