Short answer. No. Article 1758 states plainly that the reduction of fare does not justify any limitation of the common carrier's liability. Paying less for your ticket does not reduce the standard of care and responsibility the carrier owes you as a passenger for your safety during the trip.
What the law says
The reduction of fare does not justify any limitation of the common carrier's liability.
Civil Code, Article 1758 — Gratuitous Passengers. Read the full provision →
A discount does not buy the carrier a lower standard of care
Article 1758 states the rule you are asking about directly: the reduction of fare does not justify any limitation of the common carrier's liability. Buying your ticket at a discounted price does not give the bus company grounds to treat you as less entitled to safe carriage than a passenger who paid full fare. The carrier's responsibility for your safety during the trip is not scaled down simply because the price you paid was scaled down.
Why this rule sits alongside the rule on free passengers
The same article addresses an even more extreme case first: when a passenger is carried gratuitously, a stipulation limiting the common carrier's liability for negligence is valid, but not for wilful acts or gross negligence. Even a passenger riding entirely for free can only have the carrier's liability limited for ordinary negligence, never for wilful acts or gross negligence, and even then only through an actual stipulation. Since a paying passenger, even at a discount, is in a stronger position than a gratuitous one, it follows even more clearly that a mere fare reduction, without any such stipulation at all, cannot limit the carrier's liability.
Why the law draws this line
Common carriers are held to a high standard of diligence precisely because passengers entrust their safety to the carrier and often have no real ability to inspect vehicles, verify driver competence, or otherwise protect themselves during the journey. Allowing carriers to scale back their responsibility whenever they offer a promotional or discounted fare would let pricing decisions, entirely within the carrier's own control, erode the protection passengers are supposed to have, undermining the purpose of holding common carriers to that elevated standard in the first place.
What this means if you are injured on a discounted ticket
If you are injured while riding on a discounted fare, the carrier cannot point to the lower price you paid as a basis for reducing what it owes you. Your claim for injuries arising from the carrier's fault or negligence is assessed under the same standard of liability that applies to any other passenger, and the fact that your ticket happened to be discounted is not, by itself, a valid defense the carrier can raise against your claim.