This is not accurate at all. A couple moving parts here:

VA Loans, entitlement, and encumberance: as long as the original loan is in existence, it will affect the original veteran's VA entitlement for VA loans. If the loan defaults, this will directly impact the original veteran as well. The only way around this is to have the loan formally assumed by another veteran who has sufficient entitlement (the loan transfers to the new veteran's entitlement). This is also is considered a federal debt and being in default on it will affect the original veteran in other ways as well, such as being ineligible for forbearance and other loss mitigation programs on any other loans.

Credit report: this loan will continue to report on the original borrower's credit report until the creditor reports it paid off. You can try sending the bureaus a copy of the contractual agreement for the subto buyer to show that they are now legally obligated on the debt, but I have not seen any of the four bureaus accept this. This is similar to a divorce situation where one party is awarded the property and debt, but the loan remains as a trade on the other party's credit report. Even though the original party may no longer be responsible for the debt per court order, their credit is still on the line, and nonperformance on the trade in question will wreck the original borrower's credit. I have seen this happen several times, and I have seen it disputed/challenged at the bureaus, and I have seen this dispute fail every time. Anecdotal, but just my experience.

Impacts on future borrowing ability: this will vary by loan type. Fannie/Freddie have provisions for contingent liabilities that allow lenders to disregard debts that are the primary responsibility of other parties after the other party has paid the debt in question for 12 consecutive months. You will need bank statements or copies of the checks to prove this. FHA and VA have different rules. With VA, if there is any chance that you could be held to be obligated on the debt, then it gets included in DTI/residual income. I cant imagine that any competent lender will risk a buyback by allowing a subto agreement to suffice as proof that the original borrower is no longer responsible for the debt.

Guaranties and Insurance: VA and FHA loans are guaranteed/insured by agencies of the federal government. Subto's on these loans give the government standing to file suit against the parties on the loan if/when these go bad. The govt has been asleep at the wheel for a while with respect to this, but that is rapidly changing. The new administration is proactively going after these loans. Pay attention to what Pulte (FHFA director) and the other new directors are saying about fraud in the mortgage market. They're on the hunt for this kind of thing. Furthermore, if a VA or FHA loan has even gone into a workout and has received a partial claim through FHA insurance/VASP, expect the loan to be accelerated in the next 18 months if there has been a change of ownership (like in a subto deal). The servicers/subservicers on these loans are taking the brunt of this and are looking for ways to get bad loans off their books asap. I have heard directly from two different subservicer executives that they are proactively running title scrubs on these loans annually and will use the Due on Sale clause to accelerate these loans. 

Newer development with direct lenders: I have seen a couple instances now where lenders are deeming subto transactions as fraudulent and are declining refinances/new loans for the parties involved in these deals. This is more anecdotal and less likely to be widespread, but just know that it is on the radar.