After reading the available answers, I think there is a different perspective here that should be offered.
Management of a company is much more complex than singular events or policies. The direct answer to your question of, "Is this ever actually a correct line of reasoning?" is not as often as you might want because it depends on whether your values, the company values and the speaker values are aligned. Without alignment of values such as work hours, commute, management policy and expectations, conclusions are left to chance.
In your question you suggest that there may be reasons for a BYOD policy, albeit ones that do not read as if you agree or feel comfortable with it. So your question is really about understanding the corporate values and the policies that they are based on and what conclusions can be reached based on someone's experience and/or assessment of those, which requires a more open perspective than most answers seem to provide.
Some of these answers suggest that a policy or procedure can allow a listener to conclude that a company places low value on their employees, are indications of financial hardship or mismanagement, etc. In particular how a BYOD policy indicates poor management, irresponsible finances or low employee value. These answers seem to try to validate your initial position, then conclude that this is a valid approach to evaluating the company - which is just a re-incarnation of the approach you had in making the statement, not an evaluation of the approach in general.
Those answers all require leaps of logic without establishing common values between the speaker and the company. For example, if a start-up was bootstrapping their costs and asked that employees BYOD, is that short-sighted or is it prudent? If their company fails, the devices likely contain little of value. If successful, then the employees may be well rewarded (or not...) for their contribution in this manner. This may resonate better with your values, and had the question you referenced mentioned these things, the conclusions would be very different.
In your example it is a company that has been around for a while, but a new project. So maybe they hired a manager that suggested a "startup bootstrap" approach with all the risks - and benefits - to new employees? Or perhaps they are trying to take advantage of their employees, they have financial trouble, etc? The most popular answer so far makes the case that this is financially irresponsible, etc. which is supported by many assumptions in the answer statement.
Overall, here is another way of approaching the validation process. In this big world there are many companies and many people. A smart company puts together a policy that attracts the best employees for the company - which is not always the best in the industry, the best working environment, the best perks, etc. Why? This does not always align with their goals, it may not attract the right employees, they may not be able to afford "only the best," etc.
For example, a company that produces a product based on value (lowest cost) may take an approach of having generally "below average" employees with below average wages as a means of managing costs. Why not do that? Not all employees are "A" employees and not all companies need them! And these employees should not be paid the highest wages or get the best perks. Not all tasks require the smartest, best and brightest people to accomplish them. Not all employees show up to work fully engaged, spend time outside of work improving their work skills and are fully dedicated to the advancement of their career.
This is not to say that an employee is not valued and that the employee doesn't feel valued with such an arrangement. When considering job satisfaction, work-life balance and other intangible aspects, an employee that brings their own laptop to work and is not "automatically" provided one is more likely to take care of the device. And the company may hire someone that is not very experienced in technology, or trying to make a mid-career transition, and that works for them. Also, they may have other needs that requires them to have a personal laptop with them (maybe contract work?) and this policy avoids a need to carry 2 laptops constantly. The employer may be able to pay them a higher wage than they would otherwise, which they may be bound to by legal, union or other restrictions. All of which may make that a terrible environment for a "hot shot tech person" versus someone that enjoys the mix of a "startup" new project with the security of a stable company.
Also, employees have "bad moments" that frequently they do not remember or are unaware of. In an effort to manage them, policies are created. And people that implement those policies also may have bad moments or political motivations that are not motivated, endorsed or practiced by the company overall. This is the basis for your question, but it does not address the need to have aligned values regardless of anomalous instances like these.
So statements like the one you referenced can be misleading and perhaps result in a missed opportunity for you when someone else abandons the company. After all, the loss of an employee may create a void in the company that you can fill happily and successfully. However, that is not to say these statements should be ignored. As more information is provided, the probability of the accuracy of the judgment aligning with your values improves (like in this case, knowing that it is an existing company... but then also that this is a new project).
The core issue is common values. The more you know about the speaker, the circumstances, the company and the context of the statement, in addition to your ability to judge whether the statement fits in with your values, all play a role. Generally, however, statements like these "resonate" or appear to validate a feeling someone has and result in rapid conclusions that support your perspective more than it is based on sound logic. Call that "instinct" or "discrimination" or something, but there are many times life is too complex to constantly and fully evaluate all aspects of the information we are exposed to each moment.
As a side note, I came across this post: https://security.stackexchange.com/questions/102536/is-there-a-legitimate-reason-i-should-be-required-to-use-my-companys-computer
I think that clearly illustrates that there are some people that disagree with all of the "automatic" assumptions from a BYOD policy - and would actually prefer to bring their own device. Thus, the issue is a matter of aligned values.