If a staff person has to go begging to the general fund anytime a training opportunity arises this sends a clear message to them: you are taking away money from this organization's mission. Furthermore it implies a lack of interest in the continued professional development of the staff, which can be demoralizing, and a lack of understanding about the often difficult and complicated nature of fund development, which necessitates ongoing learning.
By no means do I believe a lot of money has to be set aside for training and even a modest amount can be quite meaningful if used appropriately. (By modest I mean truly modest: $100 can buy quite a few books or a webinar on a salient subject or maybe even membership in a local group for fundraising professionals.) What's most important is the act of setting aside the money--and the necessary time to engage in training--because it shows a level of professional respect for the person(s) who is endeavoring to keep your organization financially afloat. When this happens then an organization can say they invest in fundraising training.
Final thought: investment in training isn't just for paid staff or only for staff who have the words "development", "fund", or "grant" in their titles. This investment is as important (or even more important) for volunteer staff and board members. Volunteers staff deserve the utmost courtesy and respect for their devotion to an organization and one way to show this is by helping them gain new skills, connect to professionals, etc. The topic of board member involvement in fundraising is complicated and often fraught with unspoken expectations by both the organization and board members and perhaps I'll touch on this more in a future post, but suffice it to say that boards should also set aside time and money for their own fund development education. There is nothing to be lost by having more people connected with a nonprofit who understand the value, strategies, and peculiar nature of fund development.