Context. The physical mechanism responsible for the short outbursts in a recently recognised class of high mass X-ray binaries, the supergiant fast X-ray transients (SFXTs), is still unknown. Two main hypotheses have been proposed to date: the sudden accretion by the compact object of small ejections originating in a clumpy wind from the supergiant donor, or outbursts produced at (or near) the periastron passage in wide and eccentric orbits, to explain the low (∼10 32 erg s −1 ) quiescent emission. Neither proposed mechanisms explain the whole phenomenology of these sources. IGR J11215-5952, discovered in April 2005 by the INTEGRAL satellite, is a SFXT which undergoes an outburst every 329 days, a periodicity likely associated with the orbital period of the binary system. Aims. We propose a new explanation for the outburst mechanism, based on the X-ray observations of the unique SFXT known to display periodic outbursts, IGR J11215-5952. Methods. We performed three Target of Opportunity (ToO) observations with Swift, XMM-Newton and INTEGRAL at the time of the fifth outburst, expected on 2007 February 9. Swift observations of the February 2007 outburst have been reported elsewhere. Another ToO with Swift was performed in July 2007, to monitor the supposed “apastron” passage. Results. XMM-Newton observed the source on 2007 February 9, for 23 ks, at the peak of the outburst, while INTEGRAL started the observation two days later, failing to detect the source, which had already undergone the decaying phase of the fast outburst. XMM-Newton data show large variability, with a bright flare at the beginning of the observation (lasting about 1 h), followed by a lower intensity phase (about one order of magnitude fainter) with a large variability as well as low level flaring activity. The spin periodicity discovered by RXTE is confirmed, and a spin-phase spectral variability is observed and studied in detail. The Swift campaign performed in July 2007 reveals a second outburst on 2007 July 24, as bright as that observed about 165 days before. Conclusions. The new X-ray observations allow us to propose an alternative hypothesis for the outburst mechanism in SFXTs, linked to the possible presence of a second wind component, in the form of an equatorial disc from the supergiant donor. We discuss the applicability of the model to the short outburst durations of all other SFXTs, where a clear periodicity in the outbursts has not been found yet. The new outburst from IGR J11215–5952 observed in July suggests that the true orbital period is ∼165 days, instead of 329 days, as previously thought.