It would totally be possible if the options of setting up the repair and medic stations without any unit unlocked was given, like I had proposed before sturmpios receieved their overexpensive medkits.
Other factions also aren't designed to need to backtech like OKW does, which is why still linking the medis to BTG HQ is a stupid idea
It would work even better if BTG itself was reworked to be a cheaper support weapons tier with medics and the tech structure was made linear, always requiring both Mechanized and BTG, since BTG was never an equal option to Mechanized like LT is to Captain.
The options are already there, it's just that the time for reworks is over
PS: even in a strict cost comparison ignoring cost of truck and BTG setup, 10 fuel for a stationary medic station is overly expensive compared to every single faction in the game. It's not JUST the backteching, the medics themselves are overpriced beyond what should be considered justifiable
OKW's design is to have a split tech system with either weaker LVs and more infantry based play style or no healing and stronger LVs. That's the only reason why OKW has healing on their engineer starting unit. Does it work? Well, so-so. Well enough for T2 having been the meta for ages, but also not good enough that the change for easier medic access was necessary. Your suggestion might work as well, however it would make the faction closer to all others design-wise.
What would go a long way would be to reduce the price of Sturmpio medkits at vet 2-3 by 5-10 mun.
Apsrt from that, you're doing the wrong comparison regarding medic price as well: if OKW medics did not cost fuel, the price of the main tech would need to be raised to compensate. But even when applying that logic, the medics themselves are cheap as hell. 50MP and 10 FU are probably the cheapest of any faction. Compared to Soviets, you trade 10 FU for 150MP, or 100MP/60MUN/build time when comparing to OST.