I understand it can be frustrating when you feel like you're being short changed, but when viewed from a more neutral position, I don't believe you are being treated poorly.
The warranty does not cover all faults, and like all insurance products there are exclusions. If the fault is excluded, then the warranty will not pick up the cost of the repair or the diagnosis. Why would you expect that not to be the case?
1 - The roof leak is clear to see without any diagnostics.
2 - The wiper issue is something that may, or may not be covered under warranty.. (who knows?)
3 - This inspection would be carried out at no cost at the dealer I bought the car from.
The diagnostics is not to witness the symptoms, it's to identify the cause, which will enable the dealer to determine whether it's covered by the warranty, to provide a breakdown of work and parts required to repair, and finally provide a quote for the repair to whomever will pick up the bill (including a charge for the diagnostics time). At this point, the dealer has incurred a cost, i.e. The Technician's time.
Now based upon the terms of the warranty, and regardless of which official Mercedes dealership you use, if the fault and therefore the repair is covered by the warranty then the warranty company will pay for the diagnostics and repair. If it's excluded from the warranty then you will pay for the diagnostics (having previously agreed to so), and choose whether to proceed with the repair based upon the quote provided.
So if you go ahead and ask the dealer to diagnose the fault, which I believe they have already advised may not be covered by the warranty, then once diagnosed the dealership has incurred cost, the Technician's time. Depending upon your relationship with the dealership, then they may choose to either waive the diagnostic fee, or charge you for it.
You already have a relationship with the supplying dealer, and because you bought the car from them recently are much more likely to waive the diagnostic fee, and fairly likely to repair the car. This would not be under the terms of the warranty, this would be at their cost, because they sold the car to you, and soon after it developed a fault which may have been present at the time of sale.
This is not a claim under the Tier 1 warranty. This is the seller fixing an issue that they should or could have picked up prior to sale, or who wish to protect their reputation by sorting it out for you. The outcome may be the same, that is to say that the fault has been repaired, but the cost has been met by the dealer and not the warranty company.
I believe the warranty claims process on Approved Used Cars has been tightened up because it was not uncommon for dealerships to sell cars with faults on the basis that if the customer returns after the sale, then the cost could be met by the warranty company. If repaired prior to sale then the dealership meets the cost, reducing their profit on the car. Hence the warranty claims process has been tightened.
The other way to waive the diagnostics fee is to have a relationship with another dealership, who believe that your ongoing custom is worth them accepting the cost of the Technician's time without payment. If the dealership believes you'll be a returning customer who they wish to do business with, then they may waive the fee. If they don't, then they won't, i.e. you won't go back or you're more trouble than you're worth.
How long did you plan to keep the car for, and who do you plan to use for routine servicing?
Now the argument that the dealer I bought from has more of an obligation to me is (or should be) a moot point. This is because the Tier one warranty is (as MB-UK customer services informed me) offered by Mercedes Benz themselves, and as such, should have the same conditions and level of service wherever your car is taken within the network. Sadly, this is clearly not how it works.
That's not quite true, the conditions and level of service provided by the Tier 1 warranty is the same, you just don't want to have to pay for the diagnostics or subsequent repair (if not covered by the warranty), which is understandable but doesn't mean that warranty claims are in some way different depending upon the dealership used.
If for some reason a Mercedes dealership in another town owed you £100, and the diagmostics cost £110, so they said "bring your car here for diagnostics and let's call it even", then would you still question the terms and conditions of the Tier 1 warranty if your local dealer still wanted to charge you £110?