An institution rank is a not necessary a very good measure of how strong its academic programs are. The ranks take that into account, but also consider how good business it that school, how good is the connection of the institution and industry, the endowment, what do the alumni get to do with their degrees, etc.
The strong institutions are strong because they answer a need of society. For example, my graduate school had a strong chemistry program because the graduates could easily get jobs at the nearby chemical plant which was a part of a giant corporation. On the other hand, we had a so-so physics program because there were very few companies interested in what we were doing. Those few companies, however, were in microelectronics, so the few experimental groups in my department were doing that. My point is, lack of local resources was a problem.
A much worse case is my undergraduate school. The physics program shrank from 150 to 20 undergraduates per year simply because the demand for low-paid school teachers dropped significantly over the last decade. The demand for physics graduates is very small in my city because most industry is low tech, or outsourcing. This means many people with physics degrees have insecure jobs at university, or have to move abroad for work and study, or simply leave the field.
Which brings me to the professor endowment at a low ranked school. I, and a few of my colleagues, got starting grants, or just regular grants that we tried to use to form a research group. We hired students, and even postdocs, but we couldn't retain even the average ones simply because there is little opportunity in this place for a young scientist, and the salaries are small in my field. So, we get to retain only people who don't mind salaries or aren't well enough prepared and those who have no choice because of family or other issues. I got to retain no one, thus far. So, three grants so far, no group yet.
Another problem with professor endowment at a low rank institution is the biblical problem of new cloth patch on old cloth. You can put a Ferrari tire on an old Ford Escort, but it won't matter at all. The Ford drives just the same. Worse even, a strong group in a weak university stands out and attracts jealousy, and lots of it.
As an anecdote, one of my friends had a million EU starting grant he won in a national competition. The department head simply blocked all his attempts to bring new people in the group simply because he could. Not to mention the titanic amount of paperwork that the grant generated -- about two big metal closets of signed papers and reports over 3 years.
What I'm getting to is that yes, the endowment of a professor at a low rank university means a lot less than at a strong one. The low ranked university most likely has a poorly performing bureaucracy, possibly a toxic academic environment, weak connection with local industry, or nonexistent local industry, is in a relatively poor area, etc. Then, the faculty ends up squandering his endowment, because he can buy equipment (often overpriced), but can't create a research group because he can't maintain a healthy flux of people, some coming in to study, some going out to new jobs.
Oh, and a fun fact about truly low ranked places. You may get a grant now and form a decent team with reasonably good collaborations and everything, and then your country won't have another grant competition for three years just because.
Edit -- response to comment about money squandering:
For example, you get 1 million over three years. You could buy a 500k equipment you need, but you can't because you only get 333k/year which you have to spend by 31st december. The institution won't help you because it's a lot of money and complicates a lot the accounting, so you end up spending 333k on smaller stuff you don't really need. By the end of the year all money have to be spend, or returned to the government.
Sometimes, you try to buy your equipment when the project starts. You get your money, but not at the beginning of the year. You get them sometimes late in October (it happened to me and four of my colleagues twice already in three years). To buy the equipment, the law requires you to make an auction. The procedure goes for a few months, but cannot end later than 4-th December because the ministry of education must close the financial year. You lose money again, or settle for buying other stuff you don't really need.
Another way of squandering, which works especially well for research institute is paying salaries to your research team. You can't really form your own research team as a senior researcher unless you already have one. So, if you get a grant, you will need to take members of other research team an pay them to work on your project. You are lucky if you get three people whose specialization allow them to bring a meaningful contribution to your project. Nonetheless, you have to hire someone and pay them. You could try hiring new students and postdocs, but you'd be lucky if you found more than one guy at a time willing to work for the sum you're allowed to pay. So you hire one student who does something, you pay two-three guys who can help and another 4 whose only contribution is a friendly attitude. More than that, when you apply for grants you need to nominate the research team beforehand (except for postdocs and students).
After one year and half, the student leaves to study abroad, the helpful guys get involved in other projects and neglect yours, and you have a 6-12 months of funding left. Then you spend another 2 months to prepare a decent grant application to continue funding the work you started and you get a second chance at starting a group.
Another way of wasting research money is buying overpriced equipment. The local shady companies always seem to know beforehand how much money you have and make you offers for the whole sum. When the auction comes, the others magically withdraw and you are stuck with a take it or leave it bad offer. For example, not so long ago I proposed an experiment for which I needed an impedance analyzer. We got offers from the local shady scientific instruments company. They asked for 30k for the thing. Luckily the funding was withdrawn and I didn't have time to make that mistake. Quickly looking through experimental papers, I realized that similar experiments worked out very well with used 2k analyzers.