Cancellation of a contract with a plumbing company

Yes, the paragraph applies because it has already been established that it was a doorstep transaction. An offer was physically discussed and accepted in the garden. In this case, it is irrelevant that the craftsman was called by the customer.

It is different if you contact the craftsman yourself, the offer arrived by email or post, and later you place the order by phone. The conditions for a doorstep transaction are not met, and the judgment does not apply to this scenario.

The contract for work between entrepreneur and consumer is often concluded outside the entrepreneur’s business premises. Furthermore, the parties usually use so-called means of distance communication (letters, phone calls, facsimiles, emails, etc.). This results in a contract concluded outside business premises as well as a distance contract within the meaning of §§ 312b, 312c of the Building Code.

Or elsewhere:

Right of withdrawal also for on-site craft services
A withdrawal instruction must also be given to the customer by craftsmen and companies if the contract is concluded at the customer’s home “on-site” or via telephone, fax, or email. Without instruction, the customer can withdraw from the contract and the craftsman will be left with the costs. The first court ruling on this has been made!

Background:
In practice, it is common for the craftsman to visit his customer, get an overview of the required work on site, and either give a concrete offer immediately or, in the case of extensive services, send the customer an offer including a service description and cost plan by post or email afterwards. It is rare that the customer comes to the business and commissions the craftsman with the concrete work there.
On 13.06.2014, the German right of withdrawal was comprehensively reformed and consumers basically have a 14-day right of withdrawal for “contracts concluded outside business premises.” (see also “Information Obligations Leaflet”) This applies both when the contract is concluded directly in the apartment or when the offer is sent later by email or fax (= distance selling)

312c states that it must have been concluded exclusively by telephone. Once the craftsman has been on site, this paragraph is no longer applicable.

How do you respond to this argument?

312c states ... "to use exclusively remote communication means for contract negotiations and contract conclusion." Of course, a measurement may have been taken on-site beforehand. The contract application (offer) came by email, the acceptance of the contract by telephone. Consequently, from my point of view, the claim exists.

"...Partially, entrepreneurs are advised that a distance contract does not exist if the entrepreneur has inspected the situation on site, discussed it with the customer, and only afterwards made an offer from the office, on which the contract was then concluded using remote communication means. This interpretation is based on the provision in the law (§ 312c para. 1 of the Building Code) that exclusively remote communication means must be used for contract negotiations and contract conclusion if it is to be a distance contract. The provision in the law is to be understood such that not every contact between the entrepreneur and the consumer before concluding the contract is sufficient. The contact and the content of the conversations held must be directed to the intended order, and essential components of the contract must have been discussed and clarified. This certainly includes (preferably detailed) agreements about the specific work to be carried out. If the entrepreneur only inspects the premises, perhaps also measures, even in the presence of the consumer, and then prepares and sends the offer from the office, which the consumer then also accepts by distance selling, a distance contract exists. In this case, there is a lack of direct contract negotiations between the entrepreneur and the consumer."

Everything is all well and good . Convincing us, however, will benefit neither you nor the OP. Both individual cases will be decided in court unless one side gives in. Every judge interprets the law; other cases may set tendencies, but they are not binding. Exceptions are the Federal Court of Justice (BGH) and the Federal Constitutional Court (BVerfG). Don’t get me wrong, I’m not on the craftsman’s side. Still, what you and probably some judges make of the law in particularly complex cases seems somewhat impractical to me.