There are two things to consider in turn: your partner's right to stay in Sweden and your own. Even if your partner doesn't need a residence card or could reside on another basis like the Nordic agreement, they need to establish that they are making use of their freedom of movement rights for you to enjoy the same rights.
As an EU citizen, there are four ways for your wife to qualify for a right to reside in Sweden for more than three months: being a worker, a student, the partner of another EU citizen, or qualifying as an “economically non-active” resident. It's only in the latter case, staying under article 7(1)(b) of directive 2004/38/EC, that resources (and health insurance) come into play. I therefore assume your partner isn't working in Sweden as that's the only scenario in which the Swedish Migration Agency may ask either of you about financial resources.
Once your EU citizen spouse has established that she has “sufficient resources for themselves and their family members […]” then your right to stay in Sweden with her is straightforward:
- The right of residence provided for in paragraph 1 shall extend to family members who are not nationals of a Member State, accompanying or joining the Union citizen in the host Member State, provided that such Union citizen satisfies the conditions referred to in paragraph 1(a), (b) or (c).
Note that there are no additional conditions. The Union citizen needs to satisfy the conditions in article 7(1), you (their spouse) do not. You only need to establish two facts: she is making use of her freedom of movement rights (i.e. she resides in Sweden under one of the situation discussed above) and the two of you are indeed spouses living together. Any other requirement is illegal, the only valid reason to deny you the right to live with your spouse is national security and the like.
Leaving aside students and families where all members are EU citizens, there are therefore two obvious scenarios:
- Your partner works in Sweden, both of you can live in Sweden irrespective of your resources or employment situation
- Your partner has sufficient resources for the two of you, both of you can live in Sweden but you need to prove that she has sufficient resources to get your residence card
The case you found is about a slightly less obvious scenario when the EU citizen would not be able to reside as a economically non-active person without the resources of the third-country (non-EU) citizen. Even in this case the court found that it would be illegal for a country to deny this family the right to reside under EU law. But you wrote in a comment that you are relying on your wife's savings so you don't even need to rely on this case, your situation ought to be a straightforward application of article 7(2) of the directive.
By contrast, if both of you want to rely on your employment income in Sweden then you would be in an analogous situation. It ought to be possible but it's a more complex argument. The most difficult thing in this case is to secure the right to work for the non-EU citizen in the first place. Once you're working and have an income then yes, it should count but it is easier to rely on the EU citizen's savings if you can.
The Swedish Migration Agency however, states that income from partners residing in Sweden with the EU citizen does not count towards the right of residency. […] So my question is, is the Swedish Migration Agency's position legal by denying a residency card on sufficient funds from a partner income in host member state?
Without having read the decision, it that's really the sole reason they invoked then yes it is clearly illegal.
Note that Sweden has long been breaking EU freedom of movement law in other respects related to their personal number so it wouldn't be surprising if they did it in this case as well. If the website found by JBentley is anything to go by, it's also possible the Agency is breaking local law in this specific decision, something that an appeal ought to resolve.
Whether all this results from improper implementation of the directive in Swedish law, some illegal policy from the Swedish Migration Agency or a mistake in this individual decision doesn't change your rights.
