Yes, that is my understanding of it.
Remember that that is only the income side of the assessment. Assets (incl the family home) are also taken account of when calculating the contribution. For a married couple the first 72,000 of assets is ignored but above that threshold you pay a yearly contribution of up to 5% of the value of the assets per year. I presume for a married couple that would be 5% of half the value of all assets over 72,000.
For the family home, the 5% contribution stops if the person is in the nursing home for more than 3 years but for other assets its 5% per year for however long they are in the nursing home.
If the person divests himself of assets up to 5 years before he enters the nursing home, those assets (that he no longer has) can also be taken account of when calculating the contribution.