I agree to an extent, see my edit above, however there are some differences.
Bayern are less willing to break their wage structure than City for the following reasons;
1. They are in a strong position and could, in any given year, achieve domestic and international success whether they sign Sanchez or not.
2. Bayern have a very strict wage structure which is a source of pride, to the point it has stopped them signing world class/expensive talent, in favour of absorbing from Germany, in the past. Rummenigge promised not to go over €200,000 per week and, discounting bonuses, they haven't.
3. Bayern have less money in general, getting less for winning the Bundesliga than Sunderland got for getting relegated.
4. Bayern's capital almost certainly can't support the system of high-paid, aging players being shifted on loan as their performance declines, as City are following.
Ultimately, it comes down to how much City want Sanchez. We need him more and arguably have a more fluid wage structure with borderline unlimited potential, further, he wants to come and would perhaps take less to do so.
As for Arsenal, they'll drag this on but if Bayern isn't an option then they won't flush north of £50m down the toilet.