I went through this with a leasing company a few yrs ago. Their view is that it's their car and they fit whatever they like. They said the lease cost is based on them replacing tyres with the cheapest possible. I did say that it might be their car, but if they expected me to look after it nicely then some co-operation would be welcome. I used to be good to my company cars, but I ceased caring as the lease company became more and more awkward.
I spoke to the manufacturer (Peugeot) and they said that the car was tested with a certain type(s) of tyre and anything else could affect the performance of the ABS and the cars handling / roadholding. They wouldn't put anything in writing though.
I went back to the leasing company with this info and they said, OK, so what happens when a certain type (model) of tyre is unavailable, or ceases production? Fair point, really.
I raised this as a health and safety issue at work, stating that we ought to cover ourselves (the company) and not use budget tyres. Our cars are subject to hard use and we should only fit first quality, OEM standard tyres. Eventually we got the lease company to agree that would replace like for like, wherever possible.
One trick which used to work, was to go to the tyre place on a Sunday. Our lease company wasn't open so the fitter would put on whatever you asked for. They clamped down on that though, by only allowing emergency work to be done on the cars at weekends.
Looking at the age of your car, is it just coming to the end of its lease? It could be that they simply don't want to spend a lot on the car if it's shortly going back? In a fit of pique with the leasing company, I did get all 4 of my tyres changed on a car once, just a month before it was being returned.
I would also add, that I've 'opted out' of my company car, but I *much* preferred the feeling of strolling into the dealer without a care in the world about how much the service was going to cost. Now it's my car, the whole ownership thing is *much* more stressful.
Anothe point is that some manufacturers do MO (Mercedes Option) tyres, and apparently the tyres are marked with this. Mine aren't and I replaced with standard tyres as MO were not available in both the sizes used on my car. But if you happen to have MO tyres, you might be able to insist on getting the same re-fittted. MO tyres are 'characterised' specifically for MB cars (no-one really seems to know what this means in practice, even Michelin - I asked them).