What amount of share buy-backs are legitimate?
If the company has excess cash or excess liquidity that it cannot effectively deploy in capital investments, and it has reason to believe that the expected value of returns from purchasing shares will be higher than alternatives (such as buying equities or financial instruments), this would be legitimate, where "legitimate" can be defined as an increase in the long-term value for anyone holding shares in the company.

As for determining how often this is done "legitimately", as opposed to being done manipulatively in order for inside traders to profit from reducing the supply of shares and thus illegitimately driving up prices, that's a different question. 

The question of whether it is "legitimate" in terms of share buybacks giving the executive board control out of proportion to shares held, this should be considered separately from the question of whether excess cash legitimizes the buyback from a long-term profit maximization perspective.

As for the question of whether excess cash that cannot be deployed effectively is a sign of a "healthy economy" or not, this need not be determined by the observation of excess cash of a specific corporation considering share buybacks. For example, one company may have excess cash that it cannot deploy effectively in a situation where it expects to earn higher returns from a share buyback than investing in alternative financial assets or securities, without this necessarily applying on an economy-wide basis (which would contradict a variety of theoretical assumptions about financial markets always efficiently reallocating capital to its most profitable use ... but that could happen.)

Relevant regulatory approaches to "illegitimate" share buybacks could fall under shareholder rights (other shareholders would be poorly represented by executives deciding on share buybacks to temporarily inflate share prices for their personal profit), or possibly in some cases insider trading. The regulatory framework, and its application, varies across jurisdictions.